▼❖❉❊▲❖❙ ❊▲❊▼❊◆❚❆❘❊❙ ❉❊ P❊❘❈❖▲❆➬➹❖
❙❛♠✐r❛ ▼♦r❡✐r❛ ❈✉♥❤❛ ❞❡ P❛✉❧❛
❙❛♠✐r❛ ▼♦r❡✐r❛ ❈✉♥❤❛ ❞❡ P❛✉❧❛
▼❖❉❊▲❖❙ ❊▲❊▼❊◆❚❆❘❊❙ ❉❊ P❊❘❈❖▲❆➬➹❖
❚r❛❜❛❧❤♦ ❞❡ ❈♦♥❝❧✉sã♦ ❞❡ ❈✉rs♦ ❛♣r❡s❡♥t❛❞♦ ❛♦ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ●♦✐ás✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ▼❛t❡♠át✐❝❛✳
➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ▼❛t❡♠át✐❝❛ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦ ❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❱❛❧❞✐✈✐♥♦ ❱❛r❣❛s ❏ú♥✐♦r
❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳ ➱ ♣r♦✐❜✐❞♦ ❛ r❡♣r♦❞✉çã♦ t♦t❛❧ ♦✉ ♣❛r❝✐❛❧ ❞❡st❡ tr❛❜❛❧❤♦ s❡♠ ❛ ❛✉t♦r✐③❛çã♦ ❞❛ ✉♥✐✈❡rs✐❞❛❞❡✱ ❞❛ ❛✉t♦r❛ ❡ ❞♦ ♦r✐❡♥t❛❞♦r✳
❙❛♠✐r❛ ▼♦r❡✐r❛ ❈✉♥❤❛ ❞❡ P❛✉❧❛ ❣r❛❞✉♦✉✲s❡ ❡♠ ▼❛t❡♠át✐❝❛ ♥❛ ♠♦❞❛❧✐❞❛❞❡ ▲✐❝❡♥❝✐❛t✉r❛ ♣❡❧❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ●♦✐ás ❡♠ ✷✵✵✻✳
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ❉❡✉s ♣♦r t❡r ♠❡ ❞❛❞♦ s❛ú❞❡ ❡ ❢♦rç❛ ♣❛r❛ s✉♣❡r❛r ❛s ❞✐✜❝✉❧❞❛❞❡s✳
❆ ❡st❛ ✉♥✐✈❡rs✐❞❛❞❡✱ s❡✉ ❝♦r♣♦ ❞♦❝❡♥t❡✱ ❞✐r❡çã♦ ❡ ❛❞♠✐♥✐str❛çã♦ ♣❡❧❛ ♦♣♦rt✉✲ ♥✐❞❛❞❡ ❝♦♥❝❡❞✐❞❛✱ ❜❡♠ ❝♦♠♦ ❛♦ ■▼P❆ ❡ à ❈❆P❊❙✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r Pr♦❢❡ss♦r ❉♦✉t♦r ❱❛❧❞✐✈✐♥♦ ❱❛r❣❛s ❏ú♥✐♦r ♣❡❧❛ ♣❛❝✐ê♥❝✐❛ ❡ ♣❡❧♦ s✉♣♦rt❡ ❞✉r❛♥t❡ ❛ ♣r♦❞✉çã♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ❛❧é♠ ❞❡ s✉❛s ❝♦rr❡çõ❡s ❡ ✐♥❝❡♥t✐✈♦s✳
❆♦s ♠❡✉s ♣❛✐s✱ ❈r❡✉③❛ ❡ ❖s✈❛❧❞♦✱ ❡ ❛♦ ♠❡✉ ✐r♠ã♦✱ ❆♥❞ré✱ ♣❡❧♦ ❛♠♦r✱ ✐♥❝❡♥t✐✈♦ ❡ ❛♣♦✐♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧✳
❆♦ ♠❡✉ ❡s♣♦s♦ ❚✐❜ér✐♦ ❡ ❛♦ ♠❡✉ ✜❧❤♦ ❍❡♥r✐q✉❡✱ q✉❡ ♣♦r t❛♥t❛s ✈❡③❡s t✐✈❡r❛♠ q✉❡ ❧✐❞❛r ❝♦♠ ♠✐♥❤❛ ❛✉sê♥❝✐❛ ❡ s❛✉❞❛❞❡✳
❘❊❙❯▼❖
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ ❤✐stór✐❝♦ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡✱ ❜❡♠ ❝♦♠♦ ✉♠ ♣❛♥♦r❛♠❛ ❛t✉❛❧ ❞♦ ❡♥s✐♥♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♥♦ ❇r❛s✐❧✱ ❝♦♥❝❧✉✐♥❞♦ q✉❡ ❜♦❛ ♣❛rt❡ ❞♦s ❛❧✉♥♦s ♥ã♦ ❝♦♠♣r❡❡♥❞❡♠ ♦s ❝♦♥❝❡✐t♦s ❡♥✈♦❧✈✐❞♦s ❡♠ t❛❧ ❝♦♥t❡ú❞♦✳ P❛r❛ ✐st♦✱ s✉❣❡r✐♠♦s q✉❡ s❡ ✉t✐❧✐③❡ ♠♦❞❡❧♦s ❞❡ ♣❡r❝♦❧❛çã♦ ♣❛r❛ ❞❡✐①❛r ♦ ❛♣r❡♥❞✐③❛❞♦ ♠❛✐s ❛❣r❛❞á✈❡❧ ❡ ❝♦♥❝✐s♦✳ ❆ss✐♠✱ ❤á ✉♠❛ ❜r❡✈❡ ❞❡✜♥✐çã♦ ❞❡ ♣❡r❝♦❧❛çã♦✱ ♣r✐♥❝✐♣❛✐s ár❡❛s ♦♥❞❡ ❡ss❛ t❡♦r✐❛ é ✉t✐❧✐③❛❞❛ ❡ ❛♣r❡s❡♥t❛çã♦ ❞❡ ❞♦✐s ♠♦❞❡❧♦s ❜ás✐❝♦s✱ ❝♦♠ ❝á❧❝✉❧♦s ❛ ♥í✈❡❧ ❞❡ ❣r❛❞✉❛çã♦✳ ❋✐♥❛❧✐③❛♥❞♦✱ sã♦ ♣r♦♣♦st❛s ❞✉❛s ❛♣❧✐❝❛çõ❡s ❞❛ t❡♦r✐❛ ♣❛r❛ ♦ ❊♥s✐♥♦ ❇ás✐❝♦✱ ✉♠❛ ❡♥✈♦❧✈❡♥❞♦ ❝✐r❝✉✐t♦s ❡❧étr✐❝♦s ❡ ❛ ♦✉tr❛ ❛ ❜r✐♥❝❛❞❡✐r❛ ❞♦ t❡❧❡❢♦♥❡ s❡♠ ✜♦✱ ♦❜❥❡t✐✈❛♥❞♦ ✉♠ ♠❡❧❤♦r ❛♣r❡♥❞✐③❛❞♦ ♣♦r ♣❛rt❡ ❞♦s ❛❧✉♥♦s✳
❆❇❙❚❘❆❈❚
❚❤✐s ♣❛♣❡r ♣r❡s❡♥ts ❛ ❤✐st♦r② ♦❢ ♣r♦❜❛❜✐❧✐t② ❛♥❞ ❛ ❝✉rr❡♥t ♣❛♥♦r❛♠❛ ♦❢ ❡❞✉❝❛t✐♦♥ ✐♥ ❇r❛③✐❧ ✱ ❝♦♥❝❧✉❞✐♥❣ t❤❛t ♠♦st ♦❢ t❤❡ st✉❞❡♥ts ❞♦ ♥♦t ✉♥❞❡rst❛♥❞ t❤❡ ❝♦♥❝❡♣ts ✐♥✈♦❧✈❡❞ ✐♥ s✉❝❤ ❝♦♥t❡♥t✳ ❋♦r t❤✐s ✱ ✇❡ s✉❣❣❡st ②♦✉ ✉s❡ ♣❡r❝♦❧❛t✐♦♥ ♠♦❞❡❧s t♦ ❧❡❛✈❡ t❤❡ ♠♦st ♣❧❡❛s❛♥t ❛♥❞ ❝♦♥❝✐s❡ ❧❡❛r♥✐♥❣✳ ❚❤✉s✱ t❤❡r❡ ✐s ❛ ❜r✐❡❢ ❞❡✜♥✐t✐♦♥ ♦❢ ♣❡r❝♦❧❛t✐♦♥ ✱ t❤❡ ♠❛✐♥ ❛r❡❛s ✇❤❡r❡ t❤✐s t❤❡♦r② ✐s ✉s❡❞ ❛♥❞ ♣r❡s❡♥t❛t✐♦♥ ♦❢ t✇♦ ❜❛s✐❝ ♠♦❞❡❧s ✇✐t❤ ❝❛❧❝✉❧❛t✐♦♥s ❛t t❤❡ ✉♥❞❡r✲ ❣r❛❞✉❛t❡ ❧❡✈❡❧✳ ❋✐♥❛❧❧②✱ t✇♦ ❛♣♣❧✐❝❛t✐♦♥s ♦❢ t❤❡ t❤❡♦r② t♦ ❜❛s✐❝ ❡❞✉❝❛t✐♦♥ ❛r❡ ♣r♦♣♦s❛❧s✱ ♦♥❡ ✐♥✈♦❧✈✐♥❣ ❡❧❡❝tr✐❝❛❧ ❝✐r❝✉✐ts ❛♥❞ ♦t❤❡r ✇✐r❡❧❡ss ♣❤♦♥❡ ♣r❛♥❦ ✱ ❛✐♠✐♥❣ ❛ ❜❡tt❡r ❧❡❛r♥✐♥❣ ❜② st✉❞❡♥ts ✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✹✳✶ ▼♦❞❡❧♦ ❞❡ r❡❝✐♣✐❡♥t❡s ✐♥t❡r❧✐❣❛❞♦s ❡♠ sér✐❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✷ ▼♦❞❡❧♦ ❞❡ ❘❡❝✐♣✐❡♥t❡s ✐♥t❡r❧✐❣❛❞♦s ❡♠ ár✈♦r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✸ ●rá✜❝♦ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❡①t✐♥çã♦ ❡♠ ❢✉♥çã♦ ❞❡p ♣❛r❛ d= 2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✹ ●rá✜❝♦ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❡①t✐♥çã♦ ❡♠ ❢✉♥çã♦ ❞❡p ♣❛r❛ d= 2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✺✳✶ ❈✐r❝✉✐t♦ ❡♠ sér✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✺✳✷ ❈✐r❝✉✐t♦ ❡♠ ♣❛r❛❧❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✺✳✸ ❖r❣❛♥✐③❛çã♦ ❡♠ ✜❧❛ ♣❛r❛ ♦ t❡❧❡❢♦♥❡ s❡♠✲✜♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✺✳✹ ❖r❣❛♥✐③❛çã♦ ❝✐r❝✉❧❛r ♣❛r❛ ♦ t❡❧❡❢♦♥❡ s❡♠✲✜♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✺✳✺ ●rá✜❝♦ ❝♦♠♣❛r❛t✐✈♦ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
❙✉♠ár✐♦
■◆❚❘❖❉❯➬➹❖ ✶✵
✶ ❖ ❊◆❙■◆❖ ❉❊ P❘❖❇❆❇■▲■❉❆❉❊ ◆❆ ❊❉❯❈❆➬➹❖ ❇➪❙■❈❆ ✶✶
✶✳✶ ❍✐stór✐❛ ❞❛ Pr♦❜❛❜✐❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✷ ❆ Pr♦❜❛❜✐❧✐❞❛❞❡ ♥♦ ❊♥s✐♥♦ ❇ás✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷
✷ ❆ ❚❊❖❘■❆ ❉❊ P❊❘❈❖▲❆➬➹❖ ✶✺
✷✳✶ P❡r❝♦❧❛çã♦ ❡ ❊❧❡tr✐❝✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✷ P❡r❝♦❧❛çã♦ ❡ ❊♣✐❞❡♠✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✸ P❡r❝♦❧❛çã♦ ❡ P❡tró❧❡♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✹ P❡r❝♦❧❛çã♦ ❡ ❍✐❞r♦❝❛r❜♦♥❡t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✺ P❡r❝♦❧❛çã♦ ❡ ❋♦❣♦s ❋❧♦r❡st❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✻ P❡r❝♦❧❛çã♦ ❡ ❊❝♦♣❛✐s❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✼ P❡r❝♦❧❛çã♦ ❡ ❚✐♥t❛s ❈♦♥❞✉t♦r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✽ P❡r❝♦❧❛çã♦ ❡ Ó❧❡♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✾ P❡r❝♦❧❛çã♦ ❡ ❘❡❞❡ ❞❡ ❈♦♠♣✉t❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✶✵ P❡r❝♦❧❛çã♦ ❡ ❙✐st❡♠❛s ❈❡❧✉❧❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✶✶ P❡r❝♦❧❛çã♦ ❡ Pr♦♣❛❣❛çã♦ ❞❡ ❘✉♠♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✸ ❘❊❋❊❘❊◆❈■❆▲ ❚❊Ó❘■❈❖ ✷✶
✸✳✶ ❉❡✜♥✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✷ ❚❡♦r❡♠❛s✱ ▲❡♠❛s ❡ Pr♦♣♦s✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✹ ❆▲●❯◆❙ ▼❖❉❊▲❖❙ ❚❊Ó❘■❈❖❙ ✷✽
✹✳✶ Pr✐♠❡✐r♦ ▼♦❞❡❧♦✿ P❡r❝♦❧❛çã♦ P♦r ❉✉t♦s ❡♠ ❙ér✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✷ ❙❡❣✉♥❞♦ ▼♦❞❡❧♦✿ P❡r❝♦❧❛çã♦ ❡♠ ➪r✈♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✺ ❆P▲■❈❆➬Õ❊❙ ❉❆ ❚❊❖❘■❆ ❉❊ P❊❘❈❖▲❆➬➹❖ ◆❖ ❊◆❙■◆❖ ▼➱✲
❉■❖ ✹✾
✺✳✶ ❈✐r❝✉✐t♦s ❊❧étr✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✺✳✷ ❚r❛♥s♣♦rt❡ ❞❡ ■♥❢♦r♠❛çã♦✿ ❚❡❧❡❢♦♥❡ ❙❡♠ ❋✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
❙❯▼➪❘■❖ ✾
✻ ❈❖◆❙■❉❊❘❆➬Õ❊❙ ❋■◆❆■❙ ✻✵
■◆❚❘❖❉❯➬➹❖
❖ ❝♦♥t❡ú❞♦ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ✈❡♠ ❝❛❞❛ ✈❡③ ♠❛✐s ❣❛♥❤❛♥❞♦ ❡s♣❛ç♦ ♥♦s ❝✉r✲ rí❝✉❧♦s ❜r❛s✐❧❡✐r♦s✳ P♦ré♠✱ ♦ s✐♠♣❧❡s ✏tr❛♥s♠✐t✐r✑ ❞❡ ❢ór♠✉❧❛s ❡ ❝♦♥❝❡✐t♦s ♥ã♦ t♦r♥❛ s❡✉ ❛♣r❡♥❞✐③❛❞♦ ❛❣r❛❞á✈❡❧ ❡ ❝♦♥❝✐s♦✳ P❛r❛ t❛♥t♦✱ tr❛❜❛❧❤❛r ❝♦♠ ❝♦♥t❡ú❞♦s ❝♦♥t❡①t✉❛❧✐③❛❞♦s ❡ ❝♦♠ ♣♦ssí✈❡✐s ❛♣❧✐❝❛çõ❡s ♣❛❧♣á✈❡✐s ❡ ♣❛ssí✈❡✐s ❞❡ ♦❜s❡r✈❛çã♦ ❞❡ ♥♦ss♦s ❛❧✉♥♦s ❛✉①✐❧✐❛ ♥❛ ♦❜t❡♥çã♦ ❞❡ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s✳
P❛r❛❧❡❧❛♠❡♥t❡✱ ♦❜s❡r✈❛♠♦s ✉♠❛ ❡①♣❛♥sã♦✱ ❞✉r❛♥t❡ ❛s ú❧t✐♠❛s ❞é❝❛❞❛s✱ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠♦❞❡❧♦s ♠❛t❡♠át✐❝♦s ♣❛r❛ ♣❡r❝♦❧❛çã♦✱ ♦ q✉❛❧ s❡ tr❛t❛ ❞❡ ✉♠ ❞♦s ♣♦ssí✈❡✐s ♠♦❞❡❧♦s ♣r♦❜❛❜✐❧íst✐❝♦s✱ ❞❡✜♥✐❞❛ ❝♦♠✉♠❡♥t❡ ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ♦ ♠♦✈✐♠❡♥t♦ ❡ ✜❧tr❛❣❡♠ ❞❡ ✢✉✐❞♦s ♣♦r ♠❛t❡r✐❛✐s ♣♦r♦s♦s✳ ❆ ❛♣❧✐❝❛çã♦ ❞❡ s❡✉s ❝♦♥❝❡✐t♦s ❡♥❝♦♥tr❛✲s❡ ♣r❡s❡♥t❡ ♥❛s ♠❛✐s ❞✐✈❡rs❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❝♦♠♦ ♥❛ ❢ís✐❝❛✱ ❜✐♦❧♦❣✐❛✱ ✐♥❢♦r♠át✐❝❛ ❡t❝✳✱ t❡♥❞♦ s❡✉ ❛❧✐❝❡r❝❡ ♥❛s t❡♦r✐❛s ♣r♦❜❛❜✐❧íst✐❝❛s✳
❉✐❛♥t❡ ❞❡ t❛❧ ❝❡♥ár✐♦✱ é ♣♦ssí✈❡❧ ❛❧✐❛r ❡st❡s ❞♦✐s ❝♦♥❝❡✐t♦s✱ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❡ ♣❡r❝♦❧❛çã♦✱ ♥♦ ✐♥t✉✐t♦ ❞❡ ♠❡❧❤♦r❛r ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦s ❛❧✉♥♦s ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛✳ ◆♦ ❡♥t❛♥t♦✱ é ♥❡❝❡ssár✐♦ q✉❡ ♦ ♣r♦❢❡ss♦r r❡s♣♦♥sá✈❡❧ ♣♦r ♠✐♥✐str❛r t❛❧ ❝♦♥t❡ú❞♦ ❝♦♥❤❡ç❛ ❛ t❡♦r✐❛ ❞❛ ♣❡r❝♦❧❛çã♦✱ s✉❛s ❛♣❧✐❝❛çõ❡s ❡ s❛✐❜❛ ❛❞❛♣tá✲❧❛s ❛♦ ♥í✈❡❧ ❞❡ s❡✉s ❛❧✉♥♦s ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦✳
❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❛✉①✐❧✐❛r ♥❡ss❛ ❝♦♠♣r❡✲ ❡♥sã♦✱ ❛❧é♠ ❞❡ ❛♥❛❧✐s❛r ♦ ♣❛♥♦r❛♠❛ ❛t✉❛❧ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♥♦ ❇r❛s✐❧ ❡ s✉❣❡r✐r ❛♣❧✐❝❛çõ❡s ❛❞❛♣t❛❞❛s ❞❛ t❡♦r✐❛ ❞❡ ♣❡r❝♦❧❛çã♦ ❛♦s ❛❧✉♥♦s ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✱ t♦r♥❛♥❞♦✲s❡ ❛ss✐♠ ♦ ❛♣r❡♥❞✐③❛❞♦ ♥ã♦ tã♦ ❞❡s❝♦♥❡①♦ ❝♦♠ ♦ q✉❡ ❡♥❝♦♥tr❛♠♦s ❡♠ ♥♦ss♦ ❝♦t✐❞✐❛♥♦✳
❖ tr❛❜❛❧❤♦ ❡♥❝♦♥tr❛✲s❡ ♦r❣❛♥✐③❛❞♦ ❡♠ s❡✐s ❝❛♣ít✉❧♦s✳ ❖ ♣r✐♠❡✐r♦ é ❞❡st✐♥❛❞♦ à Pr♦❜❛❜✐❧✐❞❛❞❡✱ ✐♥❝❧✉✐♥❞♦ s❡✉ ❤✐stór✐❝♦ ❡ ❛ ♠❛♥❡✐r❛ ❝♦♠♦ ♦ ❝♦♥t❡ú❞♦ ❡♥❝♦♥tr❛✲s❡ ♣r❡s❡♥t❡ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ❜r❛s✐❧❡✐r❛✳ ❏á ♦ s❡❣✉♥❞♦ ❝❛♣ít✉❧♦✱ ❛❜♦r❞❛rá ❛ ❞❡✜♥✐çã♦ ❞❡ P❡r❝♦❧❛çã♦✱ ❜❡♠ ❝♦♠♦ s✉❛ ❛♣❧✐❝❛çã♦ ♥❛s ❞✐✈❡rs❛s ár❡❛s✳ ❖ t❡r❝❡✐r♦ ❡❧❡♥❝❛rá t♦❞♦ ♦ r❡❢❡r❡♥❝✐❛❧ t❡ór✐❝♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ❛ ✐♥t❡r♣r❡t❛çã♦ ❡ ❝♦♠♣r❡❡♥sã♦ ❞♦s ♠♦❞❡❧♦s ❛♣r❡s❡♥t❛❞♦s ♥❛ s❡q✉ê♥❝✐❛ ❞♦ tr❛❜❛❧❤♦✳ ❖ q✉❛rt♦ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛rá ❞♦✐s ♠♦❞❡❧♦s t❡ór✐❝♦s ❞❡ ♣❡r❝♦❧❛çã♦ à ♥í✈❡❧ ❞❡ ❣r❛❞✉❛çã♦✱ ❡♥q✉❛♥t♦ ♦ q✉✐♥t♦ ♠♦str❛rá ❞✉❛s s✉❣❡stõ❡s ❞❡ ❛♣❧✐❝❛çã♦ ♣❛r❛ ❛ ❊❞✉❝❛çã♦ ❇á✲ s✐❝❛✱ ♠❛✐s ♣r❡❝✐s❛♠❡♥t❡ à ♥í✈❡❧ ▼é❞✐♦✳ P♦r ✜♠✱ s❡rã♦ ❛♣r❡s❡♥t❛❞❛s ❛❧❣✉♠❛s ❝♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ❡ ❝♦♥❝❧✉sõ❡s ❞♦ tr❛❜❛❧❤♦ ❛q✉✐ ❞❡s❡♥✈♦❧✈✐❞♦✳
❈❛♣ít✉❧♦ ✶
❖ ❊◆❙■◆❖ ❉❊ P❘❖❇❆❇■▲■❉❆❉❊ ◆❆
❊❉❯❈❆➬➹❖ ❇➪❙■❈❆
✶✳✶ ❍✐stór✐❛ ❞❛ Pr♦❜❛❜✐❧✐❞❛❞❡
❉❡ ❛❝♦r❞♦ ❝♦♠ ❋❊❘❘❊■❘❆✱ ❛ ♣❛❧❛✈r❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ t❡♠ ♦r✐❣❡♠ ❧❛t✐♥❛ ✭♣r♦✲ ❜❛r❡✮✱ q✉❡ s✐❣♥✐✜❝❛ ✏q✉❛❧✐❞❛❞❡ ❞♦ q✉❡ é ♣r♦✈á✈❡❧✑✳ ❙❡♥❞♦ ❛ss✐♠✱ ❤á ✉♠❛ ♥♦tór✐❛ ❛ss♦❝✐❛çã♦ ❞❛ ♣❛❧❛✈r❛ ♣r♦✈á✈❡❧ à ✐♥❝❡rt❡③❛ ❞❡ ❛❝♦♥t❡❝✐♠❡♥t♦s✳
❍✐st♦r✐❝❛♠❡♥t❡✱ ❛ ♥♦çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♥❛s❝❡✉ ❝♦♠ ♦s ❝♦♠❡r❝✐❛♥t❡s ♠❛rít✐✲ ♠♦s✱ ❤á ♠❛✐s ❞❡ ✺✵✵✵ ❛♥♦s✱ q✉❛♥❞♦ ❡st❡s ✐♥st✐t✉ír❛♠ s❡❣✉r♦s ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♣r♦t❡❣❡r❡♠ s✉❛ ❛t✐✈✐❞❛❞❡ ❝♦♠❡r❝✐❛❧ ✭❙■▲❱❆✱ ✷✵✶✵✮✳ P❛r❛ t❛♥t♦✱ ❡♠❜❛s❛✈❛♠✲s❡ ❡♠ ✏❡st✐♠❛t✐✈❛s ❡♠♣í✲ r✐❝❛s ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❡♠ ❛❝✐❞❡♥t❡s ♣❛r❛ ❡st✐♣✉❧❛r❡♠ ❛s t❛①❛s ❡ ♦s ✈❛❧♦r❡s ❞❛s ♣♦ssí✈❡✐s ✐♥❞❡♥✐③❛çõ❡s✑ ✭❙■▲❱❆✱ ✷✵✶✵✱ ♣✳✽✮✳
❏á ♥♦ sé❝✉❧♦ ❳❱■■✱ q✉❛♥❞♦ ❛ ♣♦♣✉❧❛r✐❞❛❞❡ ❞♦s ❥♦❣♦s ❞❡ ❛③❛r ❡r❛ ✐♥❝♦♥t❡stá✲ ✈❡❧✱ t♦r♥♦✉✲s❡ ♥❡❝❡ssár✐♦ ❛ ❝r✐❛çã♦ ❞❡ ♠ét♦❞♦s ♣❛r❛ ❡❧❡♥❝❛r ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ ❞❡t❡r♠✐♥❛❞♦ ❡✈❡♥t♦ ♦❝♦rr❡r ♦✉ ♥ã♦✳ ❋♦✐ ❡①❛t❛♠❡♥t❡ ♥❡ss❡ ♣❡rí♦❞♦ q✉❡ ❇❧❛✐s❡ P❛s❝❛❧ ✭✶✻✷✼✲✶✻✻✷✮ ❡ P✐❡rr❡ ❋❡r♠❛t ✭✶✻✵✶✲✶✻✻✺✮ ❝♦♠❡ç❛r❛♠ ❛ tr♦❝❛r ❝♦rr❡s♣♦♥❞ê♥❝✐❛s ❛❝❡r❝❛ ❞♦ ❛ss✉♥t♦✱ ♠♦✲ ♠❡♥t♦ ❡ss❡ ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ♦ ♣✐♦♥❡✐r♦ ♥❛ ❢♦r♠✉❧❛çã♦ ❞♦s ♣r✐♥❝í♣✐♦s ❜ás✐❝♦s ❞❛ t❡♦r✐❛ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ✭❙■▲❱❆✱ ✷✵✶✵✮✳
❙❡❣✉♥❞♦ ❇❖❨❊❘ ✭✶✾✾✻✱ ♣✳ ✸✸✹✮✿
❖ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❡st❡s ❞♦✐s ♠❛t❡♠át✐❝♦s ♥ã♦ r❡❝♦rr❡✉ às ✐❞❡✐❛s ❞❡ ❈❛r❞❛♥♦ ❞❡ ✉♠ sé❝✉❧♦ ❛♥t❡s✱ q✉❡ ♣❡r♠❛♥❡❝❡r❛♠ ❡sq✉❡❝✐❞❛s ❛té ✶✻✻✸✳ ➱ só ❞❛ tr♦❝❛ ❞❡ ❝❛rt❛s s♦❜r❡ ❡st❡s ♣r♦❜❧❡♠❛s ❡ s♦❜r❡ ♦✉tr❛s q✉❡stõ❡s ❝♦♠ ❡❧❡s r❡❧❛❝✐♦♥❛❞❛s✱ q✉❡ ✈❛✐ ♥❛s❝❡r ♦ ♣♦♥t♦ ❞❡ ♣❛rt✐❞❛✱ ♦✉ s❡❥❛✱ ❛❧❣✉♥s ❢✉♥❞❛♠❡♥t♦s✱ ❞❛ ♠♦❞❡r♥❛ t❡♦r✐❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s✳ ❋❡r♠❛t ❡ P❛s❝❛❧ sã♦✱ ❡♥tã♦✱ ❝♦♥s✐❞❡r❛❞♦s ♦s ❢✉♥❞❛❞♦r❡s ❞❛ t❡♦r✐❛ ♠❛✲ t❡♠át✐❝❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s✳
❆ss✐♠ q✉❡ ♦ ♠❛t❡♠át✐❝♦ ❤♦❧❛♥❞ês ❈❤r✐st✐❛♥ ❍✉②❣❡♥s ✭✶✻✷✾✲✶✻✾✺✮ t♦♠♦✉ ❝♦✲ ♥❤❡❝✐♠❡♥t♦ ❞❡ss❛s ❝♦rr❡s♣♦♥❞ê♥❝✐❛s✱ ♣✉❜❧✐❝♦✉ ❡♠ ✶✻✺✼ ♦ ❧✐✈r♦ ❝✉❥♦ tít✉❧♦ ❡r❛ ✏❖ r❛❝✐♦❝í♥✐♦ ♥♦s ❥♦❣♦s ❞❡ ❛③❛r✑✱ t✐❞♦ ❝♦♠♦ ♦ ♣r✐♠❡✐r♦ ❛ r❡s♣❡✐t♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✱ ❝♦♥tr✐❜✉✐♥❞♦ ❛ss✐♠
❈❆P❮❚❯▲❖ ✶✳ ❖ ❊◆❙■◆❖ ❉❊ P❘❖❇❆❇■▲■❉❆❉❊ ◆❆ ❊❉❯❈❆➬➹❖ ❇➪❙■❈❆ ✶✷
♣❛r❛ q✉❡ ❛s ❞❡♠❛✐s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ t❛✐s ❝♦♠♦ ❇✐♦❧♦❣✐❛✱ ◗✉í♠✐❝❛✱ ❞❡♥tr❡ ♦✉tr❛s✱ ✉t✐❧✐③❛ss❡♠ t❛❧ t❡♦r✐❛✳
❈❛r❞❛♥♦ ✭✶✺✵✶✲✶✺✼✻✮ ❢♦✐ ✉♠ ❞♦s ♣✐♦♥❡✐r♦s ♥❛ ❞❡s❝r✐çã♦ ❞❡ ✉♠ ♠ét♦❞♦ ❡s♣❡❝í✜❝♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✳ ❊♠ s❡✉ ❧✐✈r♦ ✏❚✉❞♦ s♦❜r❡ ♦s ❥♦❣♦s ❞❡ ❛③❛r✑✱ ♣✉❜❧✐❝❛❞♦ ❡♠ ✶✻✻✺✱ ❛❧é♠ ❞❡ ❡st✉❞❛r ❛s ❧❡✐s ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡✱ ❛♥❛❧✐s❛ ♦s ❥♦❣♦s ❞❡ ❛③❛r✱ ❛✉①✐❧✐❛ ♥❛ ❝♦♠♣r❡❡♥sã♦ ❞❡st❡s ❡ ♥❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ s♦❜r❡ ❝♦♠♦ ❥♦❣❛r✳
P❡r♣❛ss❛♥❞♦ ♦s tr❛❜❛❧❤♦s ❞❡ ▲❡✐❜♥✐③ ✭✶✻✹✻✲✶✼✶✻✮✱ ❏❛q✉❡s ❇❡r♥♦✉❧❧✐ ✭✶✻✺✹✲ ✶✼✵✺✮✱ ▼♦✐✈r❡ ✭✶✻✻✼✲✶✼✺✾✮ ❡ ❚❤♦♠❛s ❇❛②❡s ✭✶✼✵✷✲✶✼✵✶✮✱ ❛ t❡♦r✐❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❢♦✐ s❡♥❞♦ ❞❡s❡♥✈♦❧✈✐❞❛✳
◆♦ ❡♥t❛♥t♦✱ s❡❣✉♥❞♦ ❇❖❨❊❘ ✭✶✶✾✻✱ ♣✳ ✸✸✹✮✿
❆ t❡♦r✐❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡✈❡ ♠❛✐s ❛ ▲❛♣❧❛❝❡ q✉❡ ❛ q✉❛❧q✉❡r ♦✉tr♦ ♠❛t❡♠át✐❝♦✳ ❆ ♣❛rt✐r ❞❡ ✶✼✼✹✱ ❡❧❡ ❡s❝r❡✈❡✉ ♠✉✐t♦s ❛rt✐❣♦s s♦❜r❡ ♦ ❛ss✉♥t♦✱ ❝✉❥♦s r❡s✉❧t❛❞♦s ✐♥❝♦r♣♦r♦✉ ♥♦ ❝❧áss✐❝♦ ❧✐✈r♦ ❚❡♦r✐❛ ❆♥❛❧ít✐❝❛ ❞❛s Pr♦❜❛❜✐❧✐❞❛❞❡s✱ ❞❡ ✶✽✶✷✳ ❊❧❡ ❝♦♥s✐❞❡r♦✉ ❛ t❡♦r✐❛ ❡♠ t♦❞♦s ♦s ❛s♣❡❝t♦s ❡ ❡♠ t♦❞♦s ♦s ♥í✈❡✐s✳
❏á ❛ r❡s♣❡✐t♦ ❞♦ ❝á❧❝✉❧♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s✱ ▲❛♣❧❛❝❡ ✭❛♣✉❞ ◆❆❙❈■▼❊◆❚❖✱ ✷✵✶✹✱ ♣✳ ✸✮ ❡s❝r❡✈❡✉✿
❆ t❡♦r✐❛ ❞❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s✱ ♥♦ ❢✉♥❞♦✱ ♥ã♦ é ♠❛✐s ❞♦ q✉❡ ♦ ❜♦♠ s❡♥s♦ tr❛❞✉③✐❞♦ ❡♠ ❝á❧❝✉❧♦ q✉❡ ♣❡r♠✐t❡ ❝❛❧❝✉❧❛r ❝♦♠ ❡①❛t✐❞ã♦ ❛q✉✐❧♦ q✉❡ ❛s ♣❡ss♦❛s s❡♥t❡♠ ♣♦r ✉♠❛ ❡s♣é❝✐❡ ❞❡ ✐♥st✐♥t♦✳ ➱ ♥❛t✉t❛❧ ❝♦♠♦ t❛❧ ❝✐ê♥❝✐❛✱ q✉❡ ❝♦♠❡ç♦✉ ❝♦♠ ❡st✉❞♦s s♦❜r❡ ❥♦❣♦s ❞❡ ❛③❛r✱ t❡♥❤❛ ❛❧❝❛♥ç❛❞♦ ♦s ♠❛✐s ❛❧t♦s ♥í✈❡✐s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❤✉♠❛♥♦✳
❏á ♥♦ ✜♥❛❧ ❞♦ sé❝✉❧♦ ❳❱■■■ ❡ ✐♥í❝✐♦ ❞♦ sé❝✉❧♦ ❳■❳✱ ♠❛t❡♠át✐❝♦s ❝♦♠♦ ▲❛❣r❛♥❣❡✱ ▲❛♣❧❛❝❡✱ ●❛✉ss✱ P♦✐ss♦♥ ❡ ❉❡ ▼♦✐✈r❡ ❝♦♥s❡❣✉✐r❛♠ ❛♣r♦❢✉♥❞❛r ♥❛ t❡♦r✐❛ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✱ ✈✐s✉❛❧✐③❛♥❞♦ ❛♣❧✐❝❛çõ❡s ♥❛s ❝✐ê♥❝✐❛s s♦❝✐❛✐s✱ ❜✐♦❧ó❣✐❝❛s ❡ ♥❛ ❢ís✐❝❛✳
❆♣❡s❛r ❞❡ ♠✉✐t♦s ❛♥♦s ❞❡ ❡st✉❞♦✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ só ❛♣❛r❡❝❡✉ ❡♠ ♥♦ss♦s ❝✉r✲ rí❝✉❧♦s ❡♠ ✶✾✾✼✱ ❝♦♠♦ s❡rá ❛♣r❡s❡♥t❛❞♦ ♥❛ ♣ró①✐♠❛ s❡çã♦✳
✶✳✷ ❆ Pr♦❜❛❜✐❧✐❞❛❞❡ ♥♦ ❊♥s✐♥♦ ❇ás✐❝♦
P❛r❛ ❝♦♠♣r❡❡♥❞❡r ♦ ♣❛♥♦r❛♠❛ ❛t✉❛❧ ❞♦ ❡♥s✐♥♦ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ♥❛ ❊❞✉❝❛çã♦ ❇ás✐❝❛ ❜r❛s✐❧❡✐r❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♥♦ ❊st❛❞♦ ❞❡ ●♦✐ás✱ é ♥❡❝❡ssár✐♦ ❝♦♥❤❡❝❡r ♦s ❞♦❝✉♠❡♥t♦s ❡ ❛ ❧❡❣✐s❧❛çã♦ ✈✐❣❡♥t❡ ♥♦ q✉❡ t❛♥❣❡ ❛ ❡st❡ ❛ss✉♥t♦✱ s❡♥❞♦ ❡❧❡s ♦s P❛râ♠❡tr♦s ❈✉rr✐❝✉❧❛r❡s ◆❛❝✐♦♥❛✐s ✲ P❈◆✬s✱ ♦s P❛râ♠❡tr♦s ❈✉rr✐❝✉❧❛r❡s ◆❛❝✐♦♥❛✐s ♣❛r❛ ♦ ❊♥s✐♥♦ ▼é❞✐♦ ✲ P❈◆❊▼✱ ▲❡✐ ❞❡ ❉✐r❡tr✐③❡s ❡ ❇❛s❡s ✲ ▲❉❇✱ ❡ ♦ ❈✉rrí❝✉❧♦ ❘❡❢❡rê♥❝✐❛ ❞♦ ❊st❛❞♦ ❞❡ ●♦✐ás✳
❆♣❡s❛r ❞❡ s❡r ✉♠ ❛ss✉♥t♦ ❞❛t❛❞♦ ❞❡ ✺✵✵✵ ❛♥♦s✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ s♦♠❡♥t❡ ❢♦✐ ✐♥s❡r✐❞❛ ❝♦♠♦ ❝♦♥t❡ú❞♦ ❡s❝♦❧❛r ❡♠ ✶✾✾✼✱ ❝♦♠ ❛ ❡❧❛❜♦r❛çã♦ ❞♦s P❈◆✬s✳ ◆❡st❡ ❞♦❝✉♠❡♥t♦✱ ♦ ❡♥s✐♥♦ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ❡stá ❛❧♦❝❛❞♦ ♥♦ ❜❧♦❝♦ ❞❡ ❝♦♥t❡ú❞♦s ❞❡♥♦♠✐♥❛❞♦ ✏❚r❛t❛♠❡♥t♦ ❞❛ ■♥❢♦r♠❛çã♦✑✳
P❛r❛ ♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧✱ ♦ ❝♦♥t❡ú❞♦ ❛♣❛r❡❝❡ ♥♦s ✸o❡ ✹o ❝✐❝❧♦s ✭✻ ❛ ✾o❆♥♦✮✳
❈❆P❮❚❯▲❖ ✶✳ ❖ ❊◆❙■◆❖ ❉❊ P❘❖❇❆❇■▲■❉❆❉❊ ◆❆ ❊❉❯❈❆➬➹❖ ❇➪❙■❈❆ ✶✸
◆❡st❡ ❝✐❝❧♦✱ t❛♠❜é♠ ❛♠♣❧✐❛✲s❡ ❛ ❡①♣❧♦r❛çã♦ ❞❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ q✉❛♥t✐✜❝❛r ♦ ✐♥❝❡rt♦✳ ❈♦♠ ❛s ♥♦çõ❡s ❡❧❡♠❡♥t❛r❡s ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♦s ❛❧✉♥♦s ❛♣r❡♥❞❡rã♦ ❛ ❞❡t❡r♠✐♥❛r ❛s ❝❤❛♥❝❡s ❞❡ ♦❝♦rrê♥❝✐❛ ❞❡ ❛❧❣✉♥s ❡✈❡♥t♦s ✭♠♦❡❞❛s✱ ❞❛❞♦s✱ ❝❛rt❛s✮✳ ❆ss✐♠✱ ♣♦❞❡rã♦ ✐r s❡ ❢❛♠✐❧✐❛r✐③❛♥❞♦ ❝♦♠ ♦ ♠♦❞♦ ❝♦♠♦ ❛ ▼❛t❡♠át✐❝❛ é ✉s❛❞❛ ♣❛r❛ ❢❛③❡r ♣r❡✈✐sõ❡s ❡ ♣❡r✲ ❝❡❜❡r ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♥❛ ✈✐❞❛ ❝♦t✐❞✐❛♥❛✳
❆♣❡s❛r ❞❡st❛ ✐♥tr♦❞✉çã♦ ♥♦ ❊♥s✐♥♦ ❋✉♥❞❛♠❡♥t❛❧✱ ❤á ✉♠❛ s✉❣❡stã♦ ❞❡ q✉❡ ♦ t❡♠❛ t❡♥❤❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞❡ ❝❛rát❡r ✐♥❢♦r♠❛❧ ♥❡st❡s ❝✐❝❧♦s✱ t❡♥❞♦ s✉❛ ❝♦♥s♦❧✐❞❛çã♦ ♥♦ ❊♥s✐♥♦ ▼é❞✐♦✳
◆♦s P❛râ♠❡tr♦s ❝✉rr✐❝✉❧❛r❡s ◆❛❝✐♦♥❛✐s ♣❛r❛ ♦ ❊♥s✐♥♦ ▼é❞✐♦ ✭P❈◆❊▼✮✱ ❞❡ ✷✵✵✵✱ ❡♥❝♦♥tr❛♠♦s ♦ ❡♥s✐♥♦ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ❝♦♠♦ ✉♠❛ ✏❝♦♠♣❡tê♥❝✐❛ ♥❛ q✉❛❧ ❞❡✈❡ s❡r ❞❡s❡♥✈♦❧✈✐❞❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ❝❛rát❡r ❛❧❡❛tór✐♦ ❡ ♥ã♦ ❞❡t❡r♠✐♥íst✐❝♦ ❞♦s ❢❡♥ô♠❡♥♦s ♥❛✲ t✉r❛✐s ❡ s♦❝✐❛✐s ❡ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✐♥str✉♠❡♥t♦s ❛❞❡q✉❛❞♦s ❞❡ ❛♠♦str❛s ❡ ❝á❧❝✉❧♦ ❞❡ ♣r♦❜❛✲ ❜✐❧✐❞❛❞❡s✳✑✭▲■▼❆✱ ✷✵✶✸✱ ♣✳ ✹✹✮
❆✐♥❞❛ s❡❣✉♥❞♦ ♦ P❈◆❊▼✱ ♦ ❡st✉❞♦ ❞❛ ❛♥á❧✐s❡ ❝♦♠❜✐♥❛tór✐❛ ❡ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ é ♣ré✲r❡q✉✐s✐t♦ ♣❛r❛ ✉♠❛ ❜♦❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ♦✉tr♦s t❡♠❛s✱ ❝♦♠♦ ❛s ❧❡✐s ❞❛ ❤❡r❡❞✐t❛r✐❡✲ ❞❛❞❡✱ ♥❛ ❇✐♦❧♦❣✐❛✱ ♣♦r ❡①❡♠♣❧♦✳
◆♦ ❛♥♦ ❞❡ ✷✵✵✼✱ ❢♦✐ ♣✉❜❧✐❝❛❞♦ ♣❡❧♦ ●♦✈❡r♥♦ ❋❡❞❡r❛❧ ✉♠ ❞♦❝✉♠❡♥t♦ ❝♦♠♣❧❡✲ ♠❡♥t❛r ❛♦ P❈◆❊▼✱ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ P❈◆✰ ✭❖r✐❡♥t❛çõ❡s ❊❞✉❝❛❝✐♦♥❛✐s ❈♦♠♣❧❡♠❡♥t❛r❡s ❛♦s P❛râ♠❡tr♦s ❈✉rr✐❝✉❧❛r❡s ◆❛❝✐♦♥❛✐s ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✮✳ ◗✉❛♥t♦ ❛♦ ❡♥s✐♥♦ ❞❡ Pr♦❜❛❜✐✲ ❧✐❞❛❞❡✱ ❙▼❖▲❊ ❡ ❉■◆■❩ ❛✜r♠❛♠ q✉❡ ✭❙▼❖▲❊ ❡ ❉■◆■❩✱ ✷✵✵✷✱ ♣✳ ✸✵✮✿
❆ ❊st❛tíst✐❝❛ ❡ ❛ Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡✈❡♠ s❡r ✈✐st❛s✱ ❡♥tã♦✱ ❝♦♠♦ ✉♠ ❝♦♥✲ ❥✉♥t♦ ❞❡ ✐❞❡✐❛s ❡ ♣r♦❝❡❞✐♠❡♥t♦s q✉❡ ♣❡r♠✐t❡♠ ❛♣❧✐❝❛r ❛ ▼❛t❡♠át✐❝❛ ❡♠ q✉❡stõ❡s ❞♦ ♠✉♥❞♦ r❡❛❧✱ ♠❛✐s ❡s♣❡❝✐❛❧♠❡♥t❡ ❛q✉❡❧❛s ♣r♦✈❡♥✐❡♥t❡s ❞❡ ♦✉tr❛s ár❡❛s✳ ❉❡✈❡♠ s❡r ✈✐st❛s t❛♠❜é♠ ❝♦♠♦ ❢♦r♠❛s ❞❡ ❛ ▼❛t❡✲ ♠át✐❝❛ q✉❛♥t✐✜❝❛r ❡ ✐♥t❡r♣r❡t❛r ❝♦♥❥✉♥t♦s ❞❡ ❞❛❞♦s ♦✉ ✐♥❢♦r♠❛çõ❡s q✉❡ ♥ã♦ ♣♦❞❡♠ s❡r q✉❛♥t✐✜❝❛❞♦s ❞✐r❡t❛ ♦✉ ❡①❛t❛♠❡♥t❡✳
❖ P❈◆✰ ❞❡✐①❛ ❝♦♠♦ s✉❣❡stã♦ q✉❡ ♦ ❡♥s✐♥♦ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ s❡❥❛ ❡❢❡t✉❛❞♦ ♥❛ ❙❡❣✉♥❞❛ ❙ér✐❡ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✱ s✉❣❡stã♦ ❡st❛ ❛❝❛t❛❞❛ ♥♦ ❈✉rrí❝✉❧♦ ❘❡❢❡rê♥❝✐❛ ❞❛ ❘❡❞❡ ❊st❛❞✉❛❧ ❞❡ ❊❞✉❝❛çã♦ ❞❡ ●♦✐ás✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❙❡❝r❡t❛r✐❛ ❊st❛❞✉❛❧ ❞❡ ❊❞✉❝❛çã♦ ❞❡ ●♦✐ás✱ t❛❧ ❝✉rrí❝✉❧♦ ❢♦✐ ✐♠♣❧❛♥t❛❞♦ ♥❛s ❡s❝♦❧❛s ❡st❛❞✉❛✐s ❡♠ ✷✵✶✸✱ ❡ t❡✈❡ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❝♦♥tr✐❜✉✐r ❝♦♠ ❛s ❯♥✐❞❛❞❡s ❊❞✉❝❛❝✐♦♥❛✐s ❛♣r❡s❡♥t❛♥❞♦ ♣r♦♣♦st❛s ❞❡ ❜✐♠❡str❛❧✐③❛çã♦ ❞♦s ❝♦♥t❡ú❞♦s ♣❛r❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❞♦ ❝✉rrí❝✉❧♦ ❡ s✉❛ ✉t✐❧✐③❛çã♦ ♥❛ s❛❧❛ ❞❡ ❛✉❧❛✳
◆❛ ✈❡r❞❛❞❡✱ ♦ ✐♥t✉✐t♦ ❢♦✐ ✉♥✐❢♦r♠✐③❛r ♦s ❝♦♥t❡ú❞♦s ♠✐♥✐str❛❞♦s✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ q✉❡ ♦ ❛❧✉♥♦✱ ❛♦ s❡ tr❛♥s❢❡r✐r ❞❡ ✉♠❛ ❡s❝♦❧❛ ♣❛r❛ ♦✉tr❛✱ ♥ã♦ s♦❢r❡ss❡ ❝♦♠ ♣❡r❞❛ ❞❡ ❝♦♥t❡ú❞♦s✳
❆ ❙♦❝✐❡❞❛❞❡ ❇r❛s✐❧❡✐r❛ ❞❡ ▼❛t❡♠át✐❝❛ ✭❙❇▼✮ ❡stá ♣r♦♣♦♥❞♦✱ ♥❡st❡ ❛♥♦ ❞❡ ✷✵✶✺✱ q✉❡ ❤❛❥❛ ✉♠❛ r❡❡str✉t✉r❛çã♦ ❞♦ ❊♥s✐♥♦ ❇ás✐❝♦✳ ◆❡st❛ ♣r♦♣♦st❛✱ ♦ ❡♥s✐♥♦ ❞❛s té❝♥✐❝❛s ❞❡ ❝♦♥t❛❣❡♠ ❛❝♦♥t❡❝❡r✐❛ ♥❛ ❙❡❣✉♥❞❛ ❙ér✐❡ ❞♦ ❊♥s✐♥♦ ▼é❞✐♦✱ ❡♥q✉❛♥t♦ ♦ ❡♥s✐♥♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛❝♦♥t❡❝❡r✐❛ s♦♠❡♥t❡ ♥❛ sér✐❡ s❡❣✉✐♥t❡✳
❈❆P❮❚❯▲❖ ✶✳ ❖ ❊◆❙■◆❖ ❉❊ P❘❖❇❆❇■▲■❉❆❉❊ ◆❆ ❊❉❯❈❆➬➹❖ ❇➪❙■❈❆ ✶✹
✭■◆❆❋✮ ♥♦s ♠♦str❛♠ ✉♠ ❣r❛♥❞❡ í♥❞✐❝❡ ❞❡ ❞❡s❝♦♥❤❡❝✐♠❡♥t♦ ♦✉ ❞✐✜❝✉❧❞❛❞❡ ❞❡ s❡ ❞♦♠✐♥❛r ❝❡rt♦ ❛ss✉♥t♦✳ ❙❡❣✉♥❞♦ ❘❊❩❊◆❉❊ ❡ ❋❊❘❘❊■❘❆ ✭✷✵✶✶✮✱ ✏♦ ❡♥s✐♥♦ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ♥❛ ❡s❝♦❧❛ ❜ás✐❝❛✱ q✉❛♥❞♦ ❛❝♦♥t❡❝❡✱ ❛✐♥❞❛ s❡ ❞á✱ ♠✉✐t❛s ✈❡③❡s✱ ✈✐♥❝✉❧❛❞♦ ❛ ❢ór♠✉❧❛s ❡ ❛ss♦❝✐❛çõ❡s ❝♦♠ s✐t✉❛çõ❡s ❝♦♥❤❡❝✐❞❛s ❡ r❡♣❡t✐❞❛s✱ q✉❛s❡ s❡♠♣r❡ ❢♦r❛ ❞❛ r❡❛❧✐❞❛❞❡ ❞♦ ❛❧✉♥♦✱ ♦ q✉❡ ♣r♦✈♦❝❛ ❞❡s✐♥t❡r❡ss❡ ♣♦r ♣❛rt❡ ❞❡st❡✑✳ ✭❘❊❩❊◆❉❊ ❡ ❋❊❘❘❊■❘❆✱ ✷✵✶✶✮✳
◆❡ss❡ s❡♥t✐❞♦✱ tr❛❜❛❧❤❛r ❛ t❡♦r✐❛ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛ss♦❝✐❛❞❛ ❛♦ ❝♦♥❝❡✐t♦ ❞❡ ♣❡r✲ ❝♦❧❛çã♦✱ t♦r♥❛ ♦ ❡st✉❞♦ ♠❛✐s ✐♥t❡r❡ss❛♥t❡✱ ✉♠❛ ✈❡③ q✉❡ s✉❛ ❛♣❧✐❝❛çã♦ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞❛ ❡♠ ✈ár✐♦s ❝❛♠♣♦s✳
❈❛♣ít✉❧♦ ✷
❆ ❚❊❖❘■❆ ❉❊ P❊❘❈❖▲❆➬➹❖
❖ ♠♦❞❡❧♦ ❞❡ P❡r❝♦❧❛çã♦ ❢♦✐ ❢♦r♠✉❧❛❞♦ ❡♠ ✜♥s ❞❛ ❞é❝❛❞❛ ❞❡ ✺✵ ♣♦r ❇r♦❛❞❜❡♥t ❡ ❍❛♠♠❡rs❧❡② ❝♦♠♦ ✉♠ ♠♦❞❡❧♦ ❞❡ tr❛♥s♣♦rt❡ ❞❡ ✢✉✐❞♦ ❡♠ ♠❡✐♦ ♣♦r♦s♦ ♦♥❞❡ ❛ ♣r♦♣❛❣❛çã♦ ❞♦s ✢✉✐❞♦s ♦❝♦rr❡ ❞❡ ✉♠❛ ❢♦r♠❛ ♥ã♦ ❧✐♥❡❛r✳ ❉❡ ❢❛t♦✱ ❡①✐st❡♠ ❞♦✐s r❡❣✐♠❡s ❜❡♠ ❞❡✜♥✐❞♦s✱ ❛ ♣r♦♣❛❣❛çã♦ ❡ ❛ ❡①t✐♥çã♦✱ s❡♣❛r❛❞♦s ♣♦r ✉♠❛ tr❛♥s✐çã♦ ❜r✉s❝❛ ✲ ❛ tr❛♥s✐çã♦ ❞❡ ♣❡r❝♦❧❛çã♦✳ ❊st❡ ♠♦❞❡❧♦ ♣♦❞❡ s❡r ❞❡s❝r✐t♦ ❝♦♠♦ ✉♠ ❞♦s ♠❛✐s s✐♠♣❧❡s ♠♦❞❡❧♦s ❞❛ ❢ís✐❝❛ ❡st❛tíst✐❝❛ ♥❛ r❡❞❡ ❛ ❡①✐❜✐r tr❛♥s✐çã♦ ❞❡ ❢❛s❡✳
❉❡ ❛❝♦r❞♦ ❝♦♠ ❋❖◆❚❊❙ ✭✶✾✾✻✮✱ ❡st❡ ♠♦❞❡❧♦ t❡✈❡ s❡✉s ♣r✐♠❡✐r♦s r❡s✉❧t❛❞♦s ♥ã♦ tr✐✈✐❛✐s ♣r♦✈❛❞♦s ♣♦r ❇r♦❛❞❜❡♥t ❡ ❍❛♠♠❡rs❧❡②✳ ❉❡s❞❡ ❡♥tã♦✱ ❡st❛ t❡♦r✐❛ ✈❡♠ s❡♥❞♦ ❞❡s❡♥✈♦❧✈✐❞❛ ❡ ♦❜s❡r✈❛❞❛ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❛♣❧✐❝❛çã♦ ❡♠ ❞✐✈❡rs❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✱ ❝♦♠♦ ❢ís✐❝❛✱ ❜✐♦❧♦❣✐❛✱ s✐st❡♠❛s ❞❡ ✐♥❢♦r♠❛çã♦ ❡t❝✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ♣❡r❝♦❧❛çã♦ ❤♦❥❡ é ✉s❛❞❛ ♣❛r❛ ❞❡s❝r❡✈❡r ♣r♦❝❡ss♦s ❞❡ ♥❛t✉r❡③❛ ❡st❛tíst✐❝❛✱ ❡ ❡stá ♠❛✐s ❛ss♦❝✐❛❞❛ ❝♦♠ ♦ ♠❡✐♦ ❞♦ q✉❡ ❝♦♠ ♦ ✢✉✐❞♦ ✭❩❆❘❆✱ ✷✵✵✵✮✳ ❆ s❡❣✉✐r✱ ♠♦str❛r❡♠♦s ❞❡ ❢♦r♠❛ s✉❝✐♥t❛ ❝♦♠♦ s✉❛ ❛♣❧✐❝❛çã♦ é ❡♥❝♦♥tr❛❞❛ ❡♠ ❛❧❣✉♠❛s s✐t✉❛çõ❡s✳ ❘❡ss❛❧t❛♠♦s q✉❡ ♦ ♦❜❥❡t✐✈♦✱ ♥❡st❡ ❝❛♣ít✉❧♦✱ ♥ã♦ é ❛♣r❡s❡♥t❛r ♦s ♠♦❞❡❧♦s ❞❡ ♣❡r❝♦❧❛çã♦ ❡♠ s✐✱ ♠❛s ✐♥❞✐❝❛r ❛s ❛♣❧✐❝❛çõ❡s ❞❡st❡ ♠♦❞❡❧♦ ❡ ❝✐t❛r tr❛❜❛❧❤♦s ♦♥❞❡ ♠❛✐♦r❡s ✐♥❢♦r♠❛çõ❡s ♣♦❞❡rã♦ s❡r ❡♥❝♦♥tr❛❞❛s✳
✷✳✶ P❡r❝♦❧❛çã♦ ❡ ❊❧❡tr✐❝✐❞❛❞❡
❉❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❆◆❊❊▲ ✭✷✵✵✽✮✱ ♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❞❛s ❡♠♣r❡s❛s ❞❡ ❞✐s✲ tr✐❜✉✐çã♦ ❞❡ ❡♥❡r❣✐❛ é ♦❢❡r❡❝❡r ✉♠ s❡r✈✐ç♦ ❝♦♥✜á✈❡❧ ❡ ❡❝♦♥ô♠✐❝♦ ♥❛ ár❡❛ ❞❡ ❝♦♥❝❡ssã♦✱ r❡s♣❡✐t❛♥❞♦ ♦s ♣❛❞rõ❡s ✐♠♣♦st♦s ♣❡❧❛ ❧❡✐ ✈✐❣❡♥t❡✳ ❉❡st❛ ♠❛♥❡✐r❛✱ q✉❛♥❞♦ ❛s ❡♠♣r❡s❛s ❝♦♥s❡❣✉❡♠ ♣r❡✈❡r s❡✉s ❡♠♣r❡❡♥❞✐♠❡♥t♦s ❢✉t✉r♦s✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡♥❡r✲ ❣✐❛ ❡❧étr✐❝❛ q✉❡ s❡rá ♥❡❝❡ssár✐❛ ❛ s❡✉s ✉s✉ár✐♦s✱ ❛ ❡♠♣r❡s❛ t❡rá ✐♥❢♦r♠❛çõ❡s ✐♠♣♦rt❛♥t❡s ♣❛r❛ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛s r❡❞❡s ❞❡ ❞✐str✐❜✉✐çã♦✱ ♣❡r♠✐t✐♥❞♦ ❛ ❛✈❛❧✐❛çã♦ ❞♦ ✈♦❧✉♠❡ ❞❡ ♦❜r❛s ♥❡❝❡ssár✐❛s ♣❛r❛ s❡✉ r❡❢♦rç♦✱ ❛♠♣❧✐❛çõ❡s ❡ ❝♦rr❡çõ❡s ❞✐✈❡rs❛s✱ ♣❛r❛ ❧❡✈❛r ❛ ❡♥❡r❣✐❛ r❡q✉❡✲ r✐❞❛ ♦♥❞❡ ❢♦r ♥❡❝❡ssár✐♦✳
❈❆P❮❚❯▲❖ ✷✳ ❆ ❚❊❖❘■❆ ❉❊ P❊❘❈❖▲❆➬➹❖ ✶✻
❚♦♠❛♥❞♦ ❝♦♠♦ ♣r♦❜❧❡♠át✐❝❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠♦❞❡❧❛r ♦ ❝r❡s❝✐♠❡♥t♦ ❡s♣❛ç♦✲ t❡♠♣♦r❛❧ ❞♦ ❝♦♥s✉♠♦ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ❞♦s ♥♦✈♦s ✉s✉ár✐♦s ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❞✐str✐❜✉✐çã♦ ♣❛r❛ ❛✉①✐❧✐❛r ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❛s ❡♠♣r❡s❛s ❞❡ ❞✐str✐❜✉✐çã♦ ❞❡ ❡♥❡r❣✐❛✱ ❆P❖▲■◆➪❘■❖✱ ❋❘❆◆❈❖ ❡ ▼❊▲❖ ✭✷✵✶✷✮ ❛♣r❡s❡♥t❛♠ ✉♠ tr❛❜❛❧❤♦ ✐♥t✐t✉❧❛❞♦ ❆♣❧✐❝❛çõ❡s ❞❛ ❚❡♦r✐❛ ❞❛ P❡r❝♦❧❛çã♦ ♥❛ ▼♦❞❡❧❛❣❡♠ ❞♦ ❈r❡s❝✐♠❡♥t♦ ❞❡ ❈❛r❣❛s ❡♠ ❙✐st❡♠❛s ❞❡ ❉✐str✐❜✉✐çã♦ ❞❡ ❊♥❡r❣✐❛ ❊❧étr✐❝❛✳
◆❡st❡ tr❛❜❛❧❤♦✱ ♦s ❛✉t♦r❡s ♠♦❞❡❧❛♠ ♦s ❛❣❧♦♠❡r❛❞♦s ♥❛ ❝✐❞❛❞❡ ❢♦r♠❛❞♦s ♣♦r ♥♦✈♦s ✉s✉ár✐♦s ❡ s❡✉ ❝r❡s❝✐♠❡♥t♦ ❞✐♥â♠✐❝♦ s❡❣✉♥❞♦ ❛ t❡♦r✐❛ ❞❛ ♣❡r❝♦❧❛çã♦✱ ✉t✐❧✐③❛♥❞♦ ♣❛r❛ ✐ss♦ ♦ ♠♦❞❡❧♦ ❞❡ ♣❡r❝♦❧❛çã♦ ♣♦r ✐♥✈❛sã♦✳ P❛r❛ ♠❛✐♦r❡s ✐♥❢♦r♠❛çõ❡s ❛❝❡r❝❛ ❞❡st❡ t✐♣♦ ❞❡ ♣❡r❝♦❧❛çã♦✱ s✉❣❡r✐♠♦s ❛ ❧❡✐t✉r❛ ❞❛ t❡s❡ ❞❡ ❩❆❘❆ ✭✶✾✾✻✮✱ ✐♥t✐t✉❧❛❞❛ P❡r❝♦❧❛çã♦ ♣♦r ✐♥✈❛✲ sã♦ ♠ú❧t✐♣❧❛✱ ❞✐s♣♦♥í✈❡❧ ♥♦ ❜❛♥❝♦ ❞❡ t❡s❡s ❞❛ ❯❙P✳
✷✳✷ P❡r❝♦❧❛çã♦ ❡ ❊♣✐❞❡♠✐❛s
❆♦ tr❛t❛r♠♦s ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❞❡ ✉♠❛ ❡♣✐❞❡♠✐❛ ❡♠ r❡❧❛çã♦ ❛ ✉♠❛ ♣♦♣✉❧❛çã♦✱ ❡stã♦ ❡♥✈♦❧✈✐❞♦s ❞♦✐s ♥í✈❡✐s ❞❡ ✐♥t❡r❛çã♦✱ ✉♠ ♠✐❝r♦s❝ó♣✐❝♦✱ q✉❡ s❡ r❡❢❡r❡ às ✐♥t❡r❛çõ❡s ❡♥tr❡ ♦ ❛❣❡♥t❡ ❝❛✉s❛❞♦r ❞❛ ❞♦❡♥ç❛ ♥♦ ✈❡t♦r ❡ ♥♦ ❤♦s♣❡❞❡✐r♦✱ ❡ ✉♠ ♠❛❝r♦s❝ó♣✐❝♦✱ ♦♥❞❡ ♦ ♣r✐♥❝✐♣❛❧ ❢❛t♦r é ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ♦s ✐♥❞✐✈í❞✉♦s ✐♥❢❡❝t❛❞♦s ❡ ♦s s✉s❝❡tí✈❡✐s ❞❡ ✐♥❢❡❝çã♦✳
❙❖❯❩❆ ✭✷✵✶✷✮✱ ❡♠ s❡✉ tr❛❜❛❧❤♦ ✐♥t✐t✉❧❛❞♦ ❚r❛♥s✐çã♦ ❞❡ ❢❛s❡s ❡♠ ♠♦❞❡❧♦s ❡st♦❝ást✐❝♦s ♣❛r❛ ❞❡s❝r❡✈❡r ❡♣✐❞❡♠✐❛s✱ ❡st✉❞❛ ♦ ♠♦❞❡❧♦ ❞❡ ❡♣✐❞❡♠✐❛ s✉s❝❡tí✈❡❧✲✐♥❢❡❝t❛❞♦✲ r❡❝✉♣❡r❛❞♦ ✭❙■❘✮ ❡st♦❝ást✐❝♦ ❡ ❡s♣❛❝✐❛❧♠❡♥t❡ ❡str✉t✉r❛❞♦✳❙❡❣✉♥❞♦ ❡st❡ ❛✉t♦r✱ ✭❙❖❯❩❆✱ ✷✵✶✷✱ ♣✳ ✺✮✿
◆❡ss❡ ♠♦❞❡❧♦✱ ♦s ✐♥❞✐✈í❞✉♦s sã♦ ❞✐✈✐❞✐❞♦s ❡♠ três ❝❧❛ss❡s✿ s✉s❝❡tí✈❡❧ ✭❙✮✱ ✐♥❢❡❝t❛❞♦ ❞❡✈✐❞♦ ❛♦ ❝♦♥t❛t♦ ❝♦♠ ✉♠ ✈✐③✐♥❤♦ ✐♥❢❡❝t❛❞♦✱ ❡ ✉♠ ✐♥❞✐✈í❞✉♦ ✐♥❢❡❝t❛❞♦ ♣♦❞❡ r❡❝✉♣❡r❛r✲s❡ ❡s♣♦♥t❛♥❡❛♠❡♥t❡✳ ❊st❡ ♠♦❞❡❧♦ ❡①✐❜❡ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ❡♠ q✉❡ ❛ ❞♦❡♥ç❛ s❡ ❡s♣❛❧❤❛ ❡ ✉♠❛ ❢❛s❡ ❡♠ q✉❡ ♥ã♦ ❤á ❡s♣❛❧❤❛♠❡♥t♦ ❞❛ ❞♦❡♥ç❛✳ ❚r❛t❛♥❞♦ ❝❛❞❛ ♣❛r s✉s❝❡tí✈❡❧✲✐♥❢❡❝t❛❞♦ ❝♦♠♦ ✉♠❛ ❝♦♥❡①ã♦ ❛tr❛✈és ❞❛ q✉❛❧ ♣♦❞❡ ❤❛✈❡r ♣r♦♣❛❣❛çã♦ ❞❛ ❡♣✐❞❡♠✐❛✱ ♠♦str❛♠♦s q✉❡ é ♣♦ssí✈❡❧ ❡st❛❜❡❧❡❝❡r ✉♠❛ ❝♦♥❡①ã♦ ❡♥tr❡ ♦ ♠♦❞❡❧♦ ❙■❘ ❡ ♦ ♠♦❞❡❧♦ ❞❡ ♣❡r❝♦❧❛çã♦✳ ❆ss✐♠✱ ♣✉❞❡♠♦s ✉t✐❧✐③❛r ♠ét♦❞♦s ❞❛ t❡♦r✐❛ ❞❡ ♣❡r❝♦❧❛çã♦ ✉s✉❛❧ ♣❛r❛ ❞❡t❡r♠✐♥❛r ♦ ❧✐♠✐❛r ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❡♣✐❞ê♠✐❝♦✳
✷✳✸ P❡r❝♦❧❛çã♦ ❡ P❡tró❧❡♦
❈❆P❮❚❯▲❖ ✷✳ ❆ ❚❊❖❘■❆ ❉❊ P❊❘❈❖▲❆➬➹❖ ✶✼
❆♣❡s❛r ❞♦ ó❧❡♦ ♣❛ss❛r ♣♦r ♠❡✐♦s ♣♦r♦s♦s ❛❧t❛♠❡♥t❡ ❤❡t❡r♦❣ê♥❡♦s✱ ❛s r♦❝❤❛s ♣♦r♦s❛s ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞❛s ❝♦♠♦ ❜♦❛s✱ ♦✉ s❡❥❛✱ ❛q✉❡❧❛s q✉❡ tê♠ ❛❧t❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✱ ❡ ❛s ❝♦♥s✐❞❡r❛❞❛s r✉✐♥s✱ ♦♥❞❡ ❤á ❜❛✐①❛ ♦✉ ♥❡♥❤✉♠❛ ♣❡r♠❡❛❜✐❧✐❞❛❞❡✳ ❈♦♠♦ ❛ ❞✐str✐❜✉✐çã♦ ❡s♣❛❝✐❛❧ ❞❡st❛s r♦❝❤❛s s❡ ❞á ❞❡ ♠❛♥❡✐r❛ ❛❧❡❛tór✐❛✱ ♣♦❞❡♠♦s ❝❛r❛❝t❡r✐③❛r ❡st❡ ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ tí♣✐❝♦ ❞❡ ♣❡r❝♦❧❛çã♦✳
✷✳✹ P❡r❝♦❧❛çã♦ ❡ ❍✐❞r♦❝❛r❜♦♥❡t♦s
❏✉♥t❛♠❡♥t❡ ❝♦♠ ♦ ❝r❡s❝✐♠❡♥t♦ ♣♦♣✉❧❛❝✐♦♥❛❧✱ ❤á ✉♠ ❛✉♠❡♥t♦ ♥❛ ❞❡♠❛♥❞❛ ❞❡ ❝♦♠❜✉stí✈❡✐s✱ ❡♠ ❡s♣❡❝✐❛❧ ❛ ❣❛s♦❧✐♥❛✳ P♦ré♠✱ q✉❛♥❞♦ ♥ã♦ ❛❝♦♥❞✐❝✐♦♥❛❞❛ ❞❡ ♠❛♥❡✐r❛ ❝♦rr❡t❛✱ ❡st❛ ❣❛s♦❧✐♥❛ ♣♦❞❡ ❝♦♥t❛♠✐♥❛r s♦❧♦ ❡ á❣✉❛ ❞✉r❛♥t❡ s❡✉ tr❛♥s♣♦rt❡ ♦✉ ❡♠ ♠ás ❝♦♥❞✐çõ❡s ❞❡ ❛r♠❛③❡♥❛♠❡♥t♦✳ ❙❡❣✉♥❞♦ ❋❖●❆➬❆ ❡t ❛❧✳ ✭✷✵✶✹✱ ♣✳ ✵✶✮✿
P♦r ♠❡✐♦ ❞❡ ♦❧❡♦❞✉t♦s ❛ ❣❛s♦❧✐♥❛ é ❝♦♥❞✉③✐❞❛ ❞❛s r❡✜♥❛r✐❛s ❛té ♦s ♣♦♥✲ t♦s ❡str❛té❣✐❝♦s ❞❡ ❞✐str✐❜✉✐çã♦ ❡ ❝♦♠❡r❝✐❛❧✐③❛çã♦✳ ❖❝♦rrê♥❝✐❛ ❞❡ ✈❛③❛✲ ♠❡♥t♦s ❡♠ ♦❧❡♦❞✉t♦s s✉❜t❡rrâ♥❡♦s ♣r♦✈♦❝❛ ❛ ❝♦♥t❛♠✐♥❛çã♦ ❞♦ s♦❧♦ ❡✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛s ❝♦♥❞✐çõ❡s ❢ís✐❝♦✲q✉í♠✐❝❛s ❞❡st❡✱ ♦ ❝♦♥t❛♠✐♥❛♥t❡ s♦❢r❡ ♣❡r❝♦❧❛çã♦✱ ♣♦❞❡♥❞♦ ❛t✐♥❣✐r r❡s❡r✈❛tór✐♦s s✉❜t❡rrâ♥❡♦s ❡✴♦✉ s✉♣❡r✜✲ ❝✐❛✐s ❞❡ á❣✉❛✱ ❝♦♠♣r♦♠❡t❡♥❞♦ ♦ ❛❜❛st❡❝✐♠❡♥t♦ ❞❡ á❣✉❛ ♣♦tá✈❡❧ ♣❛r❛ ❛s r❡❣✐õ❡s ❞♦ ❡♥t♦r♥♦✳
◆❡st❡ s❡❣♠❡♥t♦✱ ❝♦♥❤❡❝❡r ❛ t❡♦r✐❛ ❞❡ ♣❡r❝♦❧❛çã♦ ❛❥✉❞❛ ❛ ✐♠♣❡❞✐r q✉❡ ❤✐❞r♦✲ ❝❛r❜♦♥❡t♦s ❛❧❝❛♥❝❡♠ ♦ ❧❡♥ç♦❧ ❢r❡át✐❝♦✱ ❡✈✐t❛♥❞♦ ❛ss✐♠ ❛ ❝♦♥t❛♠✐♥❛çã♦ ❞❛s á❣✉❛s✳
✷✳✺ P❡r❝♦❧❛çã♦ ❡ ❋♦❣♦s ❋❧♦r❡st❛✐s
❊st✉❞❛r ❛ ❡✈♦❧✉çã♦ ❞♦s ❢♦❣♦s ✢♦r❡st❛✐s s❡ t♦r♥❛ t❛r❡❢❛ ár❞✉❛✱ ✉♠❛ ✈❡③ q✉❡ ♠ét♦❞♦s ❞❛s ❝✐ê♥❝✐❛s ❡①♣❡r✐♠❡♥t❛✐s ♥ã♦ ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞♦s✳ ◆♦ ❡♥t❛♥t♦✱ tr❛❞✉③✐♥❞♦ ♦ ♣r♦❜❧❡♠❛ ♣❛r❛ ❛ ❧✐♥❣✉❛❣❡♠ ❞❛ ♣❡r❝♦❧❛çã♦✱ ♣♦❞❡♠♦s ✉t✐❧✐③❛r ♦ ♠♦❞❡❧♦ ❞❡ ♣❡r❝♦❧❛çã♦ ❞❡ sít✐♦s✱ ♦ q✉❛❧ é ❡①♣❧✐❝❛❞♦ ♥❛ t❡s❡ ❞❡ ▲❊❇❊◆❙❩❚❆❨◆ ✭✷✵✵✷✮✱ ✐♥t✐t✉❧❛❞❛ ❖ ♠♦❞❡❧♦ ❞❡ ♣❡r✲ ❝♦❧❛çã♦ ❡♠ ❣r❛❢♦s✿ ❯♠ ❡st✉❞♦ ❞❡ ❝♦♥❞✐çõ❡s ♣❛r❛ ❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡s✱ ❞✐s♣♦♥í✈❡❧ ♥♦ ❜❛♥❝♦ ❞❡ t❡s❡s ❞❛ ❯❙P✳ P❛r❛ ❡st❡ ❡①❡♠♣❧♦✱ ❛ ✢♦r❡st❛ é r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠❛ r❡❞❡ q✉❛❞r❛❞❛ ❝♦♠ ◆ sít✐♦s✳ ❖ ❡❢❡✐t♦ ❞❛ ❞❡s♦r❞❡♠ é ♠♦❞❡❧❛❞♦ ❛tr❛✈és ❞❛ ♦❝✉♣❛çã♦ ❛❧❡❛tór✐❛ ❞❡ ✉♠❛ ❢r❛çã♦ ❞♦s sít✐♦s ❞❛ r❡❞❡✳ ❖s sít✐♦s ❡stã♦ ♦❝✉♣❛❞♦s ♣♦r ✉♠❛ ár✈♦r❡✱ ❝♦♠ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣✱ ✵≤ ♣ ≤ ✶✱ q✉❡ r❡♣r❡s❡♥t❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ✢♦r❡st❛çã♦✳ ❊♠ ♠é❞✐❛✱ p·N sít✐♦s ❡stã♦ ♦❝✉♣❛❞♦s ❡ (1−p)·N sít✐♦s ❡stã♦ ❞❡s♦❝✉♣❛❞♦s✳ ❙❡❣✉♥❞♦ ❇❆❘❘❖❙❖✱ ❡t ❛❧✳ ✭✷✵✶✵✮
❈❆P❮❚❯▲❖ ✷✳ ❆ ❚❊❖❘■❆ ❉❊ P❊❘❈❖▲❆➬➹❖ ✶✽
✷✳✻ P❡r❝♦❧❛çã♦ ❡ ❊❝♦♣❛✐s❛❣❡♠
◆♦ ❝❛♠♣♦ ❞❛ ❡❝♦♣❛✐s❛❣❡♠✱ ❛ t❡♦r✐❛ ❞❛ ♣❡r❝♦❧❛çã♦ ❢♦✐ ♠❡♥❝✐♦♥❛❞❛ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ♣♦r ●❛r❞♥❡r ❡t ❛❧ ✭✶✾✽✼✮✱ ♥❛ ♦❜r❛ ✐♥t✐t✉❧❛❞❛ ◆❡✉tr❛❧ ♠♦❞❡❧s ❢♦r t❤❡ ❛♥❛❧②s✐s ♦❢ ❜r♦❛❞✲ s❝❛❧❡ ❧❛♥❞s❝❛♣❡ ♣❛tt❡r♥✳ ◆❡st❛ ♦❜r❛✱ ♦ ♦❜❥❡t✐✈♦ ❞♦s ❛✉t♦r❡s ❡r❛ ❜✉s❝❛r ✉♠ ♠ét♦❞♦ ♣❛r❛ ❝♦♠♣r♦✈❛r s❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣❛❞rã♦ ❞❡ ♣❛✐s❛❣❡♠ ❡r❛ ♦✉ ♥ã♦ ❞❡✈✐❞♦ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❞❛❞♦ ♣r♦❝❡ss♦✳ ◆❡ss❡ s❡♥t✐❞♦✱ ❢♦r❛♠ ❝♦♥str✉í❞♦s✱ ❛ ♣❛rt✐r ❞❛s ♣r❡♠✐ss❛s ❞❛ ❚❡♦r✐❛ ❞❛ P❡r❝♦❧❛çã♦✱ ♠♦❞❡❧♦s ❞❛ ♣❛✐s❛❣❡♠ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ❡❢❡✐t♦s ❞❡ ♣r♦❝❡ss♦s ✭❡①✿ ♣❡rt✉r❜❛çõ❡s✱ ✐♥✈❛sã♦✳✳✳✮ s❡♥❞♦ ❛ss✐♠ ❞❡♥♦♠✐♥❛❞♦s ♠♦❞❡❧♦s ♥❡✉tr♦s✳ ❖s ♣❛❞rõ❡s ❣❡r❛❞♦s ♣♦r ❡ss❡s ♠♦❞❡❧♦s ❢♦r❛♠ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♣❛❞rõ❡s ❞❡ ♣❛✐s❛❣❡♠ ♦❜s❡r✈❛❞♦s✳
✷✳✼ P❡r❝♦❧❛çã♦ ❡ ❚✐♥t❛s ❈♦♥❞✉t♦r❛s
❙❡❣✉♥❞♦ ❏❯◆◗❯❊■❘❆ ✭✷✵✶✷✱ ♣✳ ✵✽✮✱
❈❤❛♠❛♠♦s ❞❡ ❝♦♠♣ós✐t♦ ❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ❞♦✐s ♦✉ ♠❛✐s ♠❛t❡r✐❛✐s ❞✐st✐♥t♦s q✉❡ ❢♦r♠❛♠ ✉♠ t❡r❝❡✐r♦ ♠❛t❡r✐❛❧✱ ♥♦ q✉❛❧ s❡✉s ❝♦♠♣♦♥❡♥t❡s ❡stã♦ s❡♣❛r❛❞♦s ❡♠ ❢❛s❡s✳ ❊ss❡ t❡r❝❡✐r♦ ♠❛t❡r✐❛❧ ❢♦r♠❛ ✉♠❛ ❝❧❛ss❡ ❞❡ ♠❛t❡r✐❛✐s ❤❡t❡r♦❣ê♥❡♦s✱ ♠✉❧t✐❢ás✐❝♦s✱ q✉❡ ♣♦❞❡♠ s❡r ♣♦❧✐♠ér✐❝♦s ♦✉ ♥ã♦✳ ❙ã♦ ♣r♦❞✉③✐❞♦s ❛rt✐✜❝✐❛❧♠❡♥t❡ ✈✐s❛♥❞♦ à ❝♦♠❜✐♥❛çã♦ ❞❛s ♠❡❧❤♦r❡s ♣r♦♣r✐❡❞❛❞❡s ❞❛s ❢❛s❡s ❝♦♥st✐t✉✐♥t❡s✳ ●❡r❛❧♠❡♥t❡✱ ✉♠❛ ❢❛s❡✱ ❛ ♠❛tr✐③✱ é ❝♦♥tí♥✉❛ ❡ ❡♥✈♦❧✈❡ ❛ ❢❛s❡ ❞✐s♣❡rs❛✳
❆♦ ❛❞✐❝✐♦♥❛r ❝❡rt❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛❧❣✉♠ t✐♣♦ ❞❡ ❝❛r❣❛ ❝♦♥❞✉t♦r❛ ❛ ✉♠❛ ♠❛tr✐③ ♣♦❧✐♠ér✐❝❛✱ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r q✉❡ ❡ss❛ ♠❛tr✐③✱ ❛♥t❡s ✐s♦❧❛♥t❡✱ ♣❛ss❛ ❛ ❝♦♥❞✉③✐r ❝♦rr❡♥t❡ ❡❧étr✐❝❛✳
❯♠ ❝♦♠♣ós✐t♦ ❝♦♥❞✉t♦r ❛♣r❡s❡♥t❛ ❞✉❛s ❢❛s❡s✱ ✉♠❛ ❝♦♥❞✉t♦r❛ ❡ ❛ ♦✉tr❛ ✐s♦✲ ❧❛♥t❡✳ ❊ss❡ t✐♣♦ ❞❡ s✐st❡♠❛ ❡①✐❜❡ ✉♠ ❧✐♠✐❛r ❞❡ ♣❡r❝♦❧❛çã♦✳ ❙❡♥❞♦ ❛ss✐♠✱ ♣❛r❛ ❝♦♠♣r❡❡♥❞❡r ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♥❞✉çã♦ ♥❡ss❡ ❝♦♠♣ós✐t♦ ❝♦♥❞✉t♦r ✉t✐❧✐③❛♠♦s ❛ t❡♦r✐❛ ❞❡ ♣❡r❝♦❧❛çã♦✱ ♣♦r ♣♦ss✐❜✐❧✐t❛r ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❝♦♥❞✉çã♦ ❡❧étr✐❝❛✳
❙❡❣✉♥❞♦ ❛ t❡♦r✐❛ ❞❡ ♣❡r❝♦❧❛çã♦✱ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ❞❡ ✉♠ ❝♦♠♣ós✐t♦ é ❞✐r❡t❛♠❡♥t❡ ❞❡♣❡♥❞❡♥t❡ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ♠❛t❡r✐❛❧ ❝♦♥❞✉t♦r ❛❞✐❝✐♦♥❛❞♦ ❛ ♠❛tr✐③ ✐s♦❧❛♥t❡✱ ❜❡♠ ❝♦♠♦ ❞❡ q✉❛♥t♦ ❝♦♥❞✉t✐✈♦ é ❡ss❡ ♠❛t❡r✐❛❧✳
❆ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♣❡r❝♦❧❛çã♦ ♥❛❞❛ ♠❛✐s s❡rá q✉❡ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ r❡❣✐ã♦ ❡st❛r ❝♦♥❡❝t❛❞❛ ❝♦♠ ♦ r❡st♦✱ ❝♦♠♣♦♥❞♦✱ ❞❡ss❛ ❢♦r♠❛✱ ✉♠❛ tr✐❧❤❛ ❝♦♥❞✉t♦r❛✳
✷✳✽ P❡r❝♦❧❛çã♦ ❡ Ó❧❡♦
❈❆P❮❚❯▲❖ ✷✳ ❆ ❚❊❖❘■❆ ❉❊ P❊❘❈❖▲❆➬➹❖ ✶✾
❡♥t❛❞❛✳ P❛r❛ ♠❛✐♦r❡s ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❡st❡ t✐♣♦ ❞❡ ♣❡r❝♦❧❛çã♦✱ s✉❣❡r✐♠♦s ❛ ❧❡✐t✉r❛ ❞❛ ♦❜r❛ ❞❡ ❙❚❖❱❊❘ ✭✶✾✾✾✮✱ ✐♥t✐t✉❧❛❞❛ ❖r✐❡♥t❡❞ P❡r❝♦❧❛t✐♦♥ ▼♦❞❡❧✳
❆ ❡s♣é❝✐❡ ❞❡ ✢✉①♦ ❡ ♦ t❛♠❛♥❤♦ ❞♦ ❞❡rr❛♠❡ ❞❡♣❡♥❞❡♠ ❞❛ ♣♦r♦s✐❞❛❞❡ ❞♦ s♦❧♦✱ q✉❡ ❞❡t❡r♠✐♥❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ♣❡r❝♦❧❛çã♦✳ ❖ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ s✐st❡♠❛ ❞❡♣❡♥❞❡ ❞❡st❛ ♣r♦❜❛❜✐❧✐❞❛❞❡✳ ❖ ♠♦❞❡❧♦ é ❝❛r❛❝t❡r✐③❛❞♦ ♣♦r ❞♦✐s r❡❣✐♠❡s✿ ✢✉①♦s ❝♦♥tí♥✉♦s ♣❛r❛ ♣♦r♦s✐❞❛❞❡s ❡❧❡✈❛❞❛s ❡ ✢✉①♦s s✉♣❡r✜❝✐❛✐s ♣❛r❛ ♣♦r♦s✐❞❛❞❡s ❜❛✐①❛s✳
✷✳✾ P❡r❝♦❧❛çã♦ ❡ ❘❡❞❡ ❞❡ ❈♦♠♣✉t❛❞♦r❡s
◆♦s ❞✐❛s ❛t✉❛✐s✱ ✈ár✐♦s s✐st❡♠❛s ❞❡ ✐♥t❡r❡ss❡ t❡❝♥♦❧ó❣✐❝♦ ❡ ❝♦♠❡r❝✐❛❧✱ t❛✐s ❝♦♠♦ ❛ ✐♥t❡r♥❡t✱ sã♦ ❡❧❡♠❡♥t♦s ❞❡ r❡❞❡s q✉❡ ♣♦❞❡♠ s❡r ❝♦♥✈❡♥✐❡♥t❡♠❡♥t❡ r❡♣r❡s❡♥t❛❞❛s ♣♦r ❣r❛❢♦s ✭♠❛✐♦r❡s ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❣r❛❢♦s s❡rã♦ ❞❛❞❛s ♥♦ ♣ró①✐♠♦ ❝❛♣ít✉❧♦✮✳
➱ ♣♦ssí✈❡❧ ✐♥✈❡st✐❣❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ ❝♦♥❡❝t✐✈✐❞❛❞❡ ❞❡s✲ t❛s r❡❞❡s ❢r❡♥t❡ à r❡♠♦çã♦ ❞❡ ❛❧❣✉♥s ❞❡ s❡✉s ✈ért✐❝❡s✳ P❛r❛ ✐ss♦✱ ♣♦❞❡✲s❡ ✉s❛r ❝♦♠♦ ❜❛s❡ ❛ t❡♦r✐❛ ❞❛ ♣❡r❝♦❧❛çã♦✱ ❝✉❥♦ ♣❛râ♠❡tr♦ ♣r✐♥❝✐♣❛❧ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ ❢r❛çã♦ ♠á①✐♠❛ ❞❡ ✈ért✐❝❡s r❡t✐r❛❞♦s ❛♥t❡s ❞❛ t♦t❛❧ ❢r❛❣♠❡♥t❛çã♦ ❞❛ r❡❞❡ ❡♠ s✉❜❣r❛❢♦s ❞❡s❝♦♥❡①♦s✳
▼❛✐♦r❡s ✐♥❢♦r♠❛çõ❡s ❛❝❡r❝❛ ❞❡ss❡ ❛ss✉♥t♦ ♣♦❞❡♠ s❡r ♦❜t✐❞❛s ♥♦ ❛rt✐❣♦ ❞❡ ▼■✲ ❈❍❊▲ ❡ ❩❆❘❆ ✭✷✵✵✹✮✱ ✐♥t✐t✉❧❛❞♦ P❡r❝♦❧❛çã♦ ❡ ❊str❛té❣✐❛s ❞❡ ❆t❛q✉❡ ❡♠ ❘❡❞❡s ❞❡ ❊s❝❛❧❛ ▲✐✈r❡✳
✷✳✶✵ P❡r❝♦❧❛çã♦ ❡ ❙✐st❡♠❛s ❈❡❧✉❧❛r❡s
❈♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♠✐♥✐♠✐③❛r ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ❡s♣❡❝tr❛❧ ❡ ❛✉♠❡♥t❛r ❛ ❝❛♣❛✲ ❝✐❞❛❞❡ ❡♠ r❡❧❛çã♦ ❛♦ ♥ú♠❡r♦ ❞❡ ✉s✉ár✐♦s ❞♦ s✐st❡♠❛✱ ❝r✐♦✉✲s❡ ❛ t❡❧❡❢♦♥✐❛ ❝❡❧✉❧❛r✳ ❉❡ss❛ ❢♦r♠❛✱ é ♦❢❡r❡❝✐❞❛ ✉♠❛ ❛❧t❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ✉s♦ ❡♠ ✉♠❛ ❧✐♠✐t❛❞❛ ❛❧♦❝❛çã♦ ❞❡ ❡s♣❡❝tr♦ ❞❡ ❢r❡q✉ê♥❝✐❛✳
❉❡✈✐❞♦ ❛♦ ❣r❛♥❞❡ ❝r❡s❝✐♠❡♥t♦ ❞❡ ✉s✉ár✐♦s ❡ ❞❛ ❞❡♠❛♥❞❛ ♣♦r s✐♥❛❧✱ ♥♦✈♦s s❡r✲ ✈✐ç♦s ❞❡ tr❛♥s♠✐ssã♦ ❢♦r❛♠ ❝r✐❛❞♦s✳ ❯♠ ❞♦s t✐♣♦s ❞❡ ♣r♦♣❛❣❛çã♦ ❞❛s ♦♥❞❛s é ✈✐❛ rá❞✐♦✱ s❡♥❞♦ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡rr❡♥♦✱ s❡ é ♣❧❛♥♦✱ ♠♦♥t❛♥❤♦s♦✱ ❝♦♠ ❝✉r✈❛s ❡ â♥❣✉❧♦s ❞❡ s✉❜✐❞❛ ♦✉ ❞❡s❝✐❞❛✱ ❡✱ ❞♦s ♦❜stá❝✉❧♦s✱ t❛✐s ❝♦♠♦✱ ❡❞✐✜❝❛çõ❡s✱ ár✈♦r❡s✱ ✈❡í❝✉❧♦s ❡ ♣❡ss♦❛s✳ ❆s ♣❡r❞❛s ❝❛✉s❛❞❛s ♣❡❧❛ ♣r♦♣❛❣❛çã♦ ♣♦r ♠ú❧t✐♣❧♦s ♣❡r❝✉rs♦s ❡ ♣❡❧♦ s♦♠❜r❡❛♠❡♥t♦ ❛❢❡t❛♠ ❛ ár❡❛ ❞❡ ❝♦❜❡rt✉r❛ ❞♦ s✐♥❛❧ ❡ ♣♦❞❡♠ r❡s✉❧t❛r ❡♠ ❡rr♦s ❞❡ ❞❡❝♦❞✐✜❝❛çã♦✳
❈❆P❮❚❯▲❖ ✷✳ ❆ ❚❊❖❘■❆ ❉❊ P❊❘❈❖▲❆➬➹❖ ✷✵
❡♠ t♦❞❛s ❛s ❞✐r❡çõ❡s✳
▼❛✐♦r❡s ✐♥❢♦r♠❛çã♦ ❛❝❡r❝❛ ❞♦ ❛ss✉♥t♦ ♣♦❞❡rã♦ s❡r ❡♥❝♦♥tr❛❞❛s ♥❛ ❞✐ss❡rt❛çã♦ ❞❡ ❋❊❘❘❊■❘❆ ✭✷✵✶✵✮ ✐♥t✐t✉❧❛❞❛ ■♥✢✉ê♥❝✐❛ ❞♦ ❊①❝❡ss♦ ❞❡ ❆tr❛s♦ ❞♦ ❈❛♥❛❧ ♥❛ ❚❛①❛ ❞❡ ❚r❛♥s♠✐ssã♦ ♣❛r❛ ♦ P❧❛♥❡❥❛♠❡♥t♦ ❞❡ ❙✐st❡♠❛s ❈❡❧✉❧❛r❡s✳
✷✳✶✶ P❡r❝♦❧❛çã♦ ❡ Pr♦♣❛❣❛çã♦ ❞❡ ❘✉♠♦r❡s
❯♠❛ ♦✉tr❛ ♣♦ssí✈❡❧ ❛♣❧✐❝❛çã♦ ♣❛r❛ ❛ t❡♦r✐❛ ❞❛ ♣❡r❝♦❧❛çã♦ é ♥♦ ❡st✉❞♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❡ r✉♠♦r❡s✱ ✉t✐❧✐③❛♥❞♦ ♣r♦❝❡ss♦s ❞❡ ♠♦❞❡❧❛❣❡♠ ♣❛r❛ r❡♣r❡s❡♥t❛r ❝♦♠♦ ♦ r✉♠♦r s❡ ❡s♣❛❧❤❛✳
❆ ♣r♦♣❛❣❛çã♦ ❞❡ r✉♠♦r❡s é ✉♠ ♣r♦❝❡ss♦ ❝♦♠✉♥✐❝❛❝✐♦♥❛❧✱ ♣r♦♠♦✈✐❞❛ ♣❡❧♦ ❝♦✲ ❧❡t✐✈♦✳ P♦❞❡ s❡r ❞❡s❝r✐t❛✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❘❊❯▲❊ ✭✷✵✵✽✱ ♣❛❣✳ ✵✺✮✱ ❝♦♠♦✿
✉♠ t✐♣♦ ❞❡ ✐♥❢♦r♠❛çã♦ ♥ã♦ ❝♦♥✜r♠❛❞❛ q✉❡ s❡ ♣r♦♣❛❣❛ ❡♠ r❡❞❡ ❡ q✉❡ ❝✐r❝✉❧❛ ❝♦♠ ❛ ✐♥t❡♥çã♦ ❞❡ s❡r t♦♠❛❞❛ ❝♦♠♦ ✈❡r❞❛❞❡✐r❛✳ ❆♣❡s❛r ❞❡ ♣♦❞❡r s❡r ✐♥♦❢❡♥s✐✈♦✱ ♦ r✉♠♦r t❛♠❜é♠ ♣♦❞❡ s❡r ♣r❡❥✉❞✐❝✐❛❧✱ ❣❡r❛♥❞♦ ❣r❛✈❡s ❝♦♥s❡qüê♥❝✐❛s q✉❛♥❞♦ s❡ tr❛t❛ ❞❡ ✉♠❛ ✐♥❢♦r♠❛çã♦ ❢❛❧s❛✳ ◆❡st❛ ❝♦♥❞✐çã♦✱ s✉❛ ❞✐ss❡♠✐♥❛çã♦ ♥✉♠ ❝♦r♣♦ s♦❝✐❛❧ ♣♦❞❡ s❡r ♠♦t✐✈♦ ❞❡ ♣r❡✲ ♦❝✉♣❛çã♦✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ r❛♣✐❞❡③ ❝♦♠ q✉❡ ❡❧❡ é ♣❛ss❛❞♦ ❛❞✐❛♥t❡ ❡ ❞❛ ❞✐♠❡♥sã♦ ❛❧❝❛♥ç❛❞❛✳
❈❛♣ít✉❧♦ ✸
❘❊❋❊❘❊◆❈■❆▲ ❚❊Ó❘■❈❖
◆❡st❡ ❝❛♣ít✉❧♦ ❡♥❝♦♥tr❛♠♦s t♦❞❛s ❛s ❞❡✜♥✐çõ❡s✱ t❡♦r❡♠❛s ❡ ❧❡♠❛s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦s ♠♦❞❡❧♦s t❡ór✐❝♦s ❛♣r❡s❡♥t❛❞♦s à ❢r❡♥t❡✳ ❆s ❞❡♠♦♥str❛çõ❡s ❞♦s t❡♦r❡♠❛s ❡ ❧❡♠❛s ❢♦r❛♠ ♦♠✐t✐❞❛s✱ ♣♦ré♠ ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞❛s ❡♠ ▲❊❇❊◆❙❩❚❆❨◆✭✷✵✶✷✮✱ ●❘❆❉❙❍❚❊❨◆ ❡ ❘❨❩❍■❑ ✭✷✵✵✼✮ ❡ ❋❊❖❋■▲❖❋❋✱ ❑❖❍❆❨❆✲ ❑❆❲❆ ❡ ❲❆❑❆❇❆❨❆❙❍■ ✭✷✵✵✶✮✳
✸✳✶ ❉❡✜♥✐çõ❡s
❉❡✜♥✐çã♦ ✶ ✭❊①♣❡r✐♠❡♥t♦ ❛❧❡❛tór✐♦✮✳ ❙ã♦ ❡①♣❡r✐♠❡♥t♦s q✉❡ ❛♦ s❡r❡♠ r❡♣❡t✐❞♦s ♥❛s ♠❡s✲ ♠❛s ❝♦♥❞✐çõ❡s ♥ã♦ ♣r♦❞✉③❡♠ ♦ ♠❡s♠♦ r❡s✉❧t❛❞♦✳
❉❡✜♥✐çã♦ ✷ ✭❊s♣❛ç♦ ❆♠♦str❛❧✮✳ ❉❡♥♦♠✐♥❛♠♦s ❡s♣❛ç♦ ❛♠♦str❛❧ ♦ ❝♦♥❥✉♥t♦ ❞❡ t♦❞♦s ♦s r❡s✉❧t❛❞♦s ♣♦ssí✈❡✐s ❞❡ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❛❧❡❛tór✐♦✱ ❡ ❞❡♥♦t❛♠♦s ♣♦r Ω✳ ❯♠ s✉❜❝♦♥❥✉♥t♦ A⊂Ωé ❝❤❛♠❛❞♦ ❡✈❡♥t♦✳
❉❡✜♥✐çã♦ ✸✳ ❆ r❡✉♥✐ã♦ ❞❡n❡✈❡♥t♦s é ♦ ❡✈❡♥t♦ q✉❡ ♦❝♦rr❡ s❡ ♣❡❧♦ ♠❡♥♦s ✉♠ ❞❡❧❡s ♦❝♦rr❡✱ ❡ ❡s❝r❡✈❡♠♦s ❛ss✐♠ ❛ ♦♣❡r❛çã♦✿ A1∪A2∪ · · · ∪An✳
❉❡✜♥✐çã♦ ✹✳ ❆ ✐♥t❡rs❡çã♦ ❞❡ n ❡✈❡♥t♦s é ♦ ❡✈❡♥t♦ q✉❡ ♦❝♦rr❡ s❡ t♦❞♦s ❡❧❡s ♦❝♦rr❡♠✱ ❡ ❡s❝r❡✈❡♠♦s ❛ss✐♠ ❛ ♦♣❡r❛çã♦✿ A1∩A2∩ · · · ∩An✳
❉❡✜♥✐çã♦ ✺✳ ❖ ❝♦♠♣❧❡♠❡♥t❛r ❞❡ ✉♠ ❡✈❡♥t♦ ❆ é ♦ ❡✈❡♥t♦ q✉❡ ♦❝♦rr❡ s❡ ❆ ♥ã♦ ♦❝♦rr❡✱ ❡ ❡s❝r❡✈❡♠♦s ❛ss✐♠ ❛ ♦♣❡r❛çã♦✿ Ac✳
❉❡✜♥✐çã♦ ✻✳ ❆ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❞♦✐s ❡✈❡♥t♦s ❆ ❡ ❇ é ♦ ❡✈❡♥t♦ q✉❡ ♦❝♦rr❡ s❡ s♦♠❡♥t❡ ❆ ♦❝♦rr❡ ❡ ❇ ♥ã♦ ♦❝♦rr❡✱ ❡ ❡s❝r❡✈❡♠♦s ❛ss✐♠ ❛ ♦♣❡r❛çã♦✿ A|B ♦✉A∩Bc✳
▲❡✐s ❞❡ ❉❡ ▼♦r❣❛♥✿
❈❆P❮❚❯▲❖ ✸✳ ❘❊❋❊❘❊◆❈■❆▲ ❚❊Ó❘■❈❖ ✷✷
n
[
i=1
Ai
!c =
n
\
i=1
Aci;
n
\
i=1
Ai
!c =
n
[
i=1
Aci.
❉❡✜♥✐çã♦ ✼✳ ❯♠❛ ❝❧❛ss❡ ❞❡ ❡✈❡♥t♦s ❛❧❡❛tór✐♦s é ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡✈❡♥t♦s ✭♦✉ s✉❜❝♦♥❥✉♥✲ t♦s✮ ❞♦ ❡s♣❛ç♦ ❛♠♦str❛❧ q✉❡ s❛t✐s❢❛③✿
✶✳ Ω∈ F ✱φ ∈ F❀
✷✳ A ∈ F ⇒Ac ∈ F❀
✸✳ ❙❡ An∈ F ♣❛r❛ n= 1,2,3, ...,❡♥tã♦
∞
[
n=1
An∈ F.
P❛r❛ ♦ ❝❛s♦ ❡♠ q✉❡ ♦ ❡s♣❛ç♦ ❛♠♦str❛❧ é ❡♥✉♠❡rá✈❡❧✱ ♣♦❞❡♠♦s ❡s❝r❡✈❡rΩ❝♦♠♦ Ω ={ω1, ω2, ω3,· · · }❡ s❡♥❞♦ A ❡♠ F✱ ❡♥tã♦
P(A) = X
i:ωi∈A
p(ωi)
❡♠ q✉❡ p(ωi) r❡♣r❡s❡♥t❛ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞♦ ❡✈❡♥t♦ s✐♠♣❧❡s✱p(ωi)≥0❡
P∞
i=1p(ωi) = 1✳
❉❡✜♥✐çã♦ ✽ ✭❉❡✜♥✐çã♦ ❝❧áss✐❝❛ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✮✳ ❙❡❥❛ ✉♠ ❡s♣❛ç♦ ❛♠♦str❛❧ Ω ❝♦♠ N r❡s✉❧t❛❞♦s ♣♦ssí✈❡✐s ✭❝❤❛♠❛❞♦s ❡✈❡♥t♦s s✐♠♣❧❡s✮✱ t♦❞♦s ❡q✉✐♣r♦✈á✈❡✐s✳ ❙❡❥❛ ❛✐♥❞❛ A ✉♠ ❡✈❡♥t♦ ❝♦♠ ✉♠ t♦t❛❧ ❞❡m❡✈❡♥t♦s s✐♠♣❧❡s✳ ❊♥tã♦✱ ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ A✱ ❞❡♥♦t❛❞❛P(A)✱ é ❞❡✜♥✐❞❛ ♣♦r✿
P(A) = m N✳
❉❡✜♥✐çã♦ ✾ ✭❉❡✜♥✐çã♦ ❋r❡q✉❡♥t✐st❛ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡✮✳ ❙❡❥❛ A ✉♠ ❡✈❡♥t♦ ❛❧❡❛tór✐♦ r❡✲ ❧❛t✐✈♦ ❛ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❛❧❡❛tór✐♦✳ ❙✉♣♦♥❤❛♠♦s q✉❡ ❡st❡ ❡①♣❡r✐♠❡♥t♦ é r❡♣❡t✐❞♦ n ✈❡③❡s ♥❛s ♠❡s♠❛s ❝♦♥❞✐çõ❡s✳ ❆ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡A ♣♦❞❡ s❡r ❞❡✜♥✐❞❛ ❝♦♠♦
P(A) = lim
n→∞
n(A)
n = limn→∞fn,A,
♦♥❞❡ fn,A é ❞❡♥♦♠✐♥❛❞❛ ❢r❡q✉ê♥❝✐❛ r❡❧❛t✐✈❛ ❞❡ A ♥❛s n r❡♣❡t✐çõ❡s ❞♦ ❡①♣❡r✐♠❡♥t♦✱ ♦♥❞❡
n(A) r❡♣r❡s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ r❡♣❡t✐çõ❡s q✉❡ ♦ ❡✈❡♥t♦ A ❛ss♦❝✐❛❞♦ ❛ ❡ss❡ ❡①♣❡r✐♠❡♥t♦ ♦❝♦rr❡ ❛♣ósn r❡♣❡t✐çõ❡s ❞♦ ❡①♣❡r✐♠❡♥t♦ ❛❧❡❛tór✐♦✳
❖❜s❡r✈❛çã♦✿ ■♥t✉✐t✐✈❛♠❡♥t❡✱ ✐ss♦ s✐❣♥✐✜❝❛ q✉❡ s❡ n é ❣r❛♥❞❡✱ P(A)≃ n(A)
❈❆P❮❚❯▲❖ ✸✳ ❘❊❋❊❘❊◆❈■❆▲ ❚❊Ó❘■❈❖ ✷✸
✶✳ 0≤P(A)≤1✱ ∀A∈ F❀
✷✳ P(Ω) = 1❀
✸✳ ❆❞✐t✐✈✐❞❛❞❡ ❡♥✉♠❡rá✈❡❧✿ ♣❛r❛ q✉❛❧q✉❡r s❡q✉ê♥❝✐❛ A1✱ A2✱ ... ∈ F ❞❡ ❞♦✐s ❡✈❡♥t♦s
❞♦✐s ❛ ❞♦✐s ❞✐s❥✉♥t♦s✱
P
∞
[
i=1
Ai
!
=
∞
X
i=1
P(Ai)✳
❆ tr✐♣❧❛ ✭Ω✱F✱ P ✮ é ❝❤❛♠❛❞❛ ✉♠ ❡s♣❛ç♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✳
❉❡✜♥✐çã♦ ✶✶✳ ❙❡❥❛♠A❡ B ❡✈❡♥t♦s ❞❡ Ω✱ ❡s♣❛ç♦ ❛♠♦str❛❧✳ A❡B sã♦ ❞✐t♦s ✐♥❞❡♣❡♥❞❡♥✲ t❡s s❡ ❡ s♦♠❡♥t❡ s❡✿ P(A∩B) = P(A)·P(B)❀
❉❡✜♥✐çã♦ ✶✷✳ ❯♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛X ❡♠ ✉♠ ❡s♣❛ç♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡(Ω,F, P)é ✉♠❛ ❢✉♥çã♦ ❛ ✈❛❧♦r❡s r❡❛✐s ❞❡✜♥✐❞❛ ❡♠Ω ✱ t❛❧ q✉❡
{X ≤x}={ω ∈Ω :X(ω)≤x} ∈ F
♣❛r❛ t♦❞♦X ∈R✳
◆❛ ❞❡✜♥✐çã♦ ❛❝✐♠❛✱{X ≤x} ∈ Fs✐❣♥✐✜❝❛ q✉❡{X ≤x}é ✉♠ ❡✈❡♥t♦ ❛❧❡❛tór✐♦✳
❙❡ ♦s ✈❛❧♦r❡s ❛ss✉♠✐❞♦s ♣♦r X sã♦ ✜♥✐t♦s ♦✉ ✐♥✜♥✐t♦s ❡♥✉♠❡rá✈❡✐s✱ ❡♥tã♦ ❞✐✲ ③❡♠♦s q✉❡ X é ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❞✐s❝r❡t❛✱ ♠❛s s❡ X ❛ss✉♠❡ ✈❛❧♦r❡s ♥✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ♥ú♠❡r♦s r❡❛✐s✱ ❡♥tã♦ ❞✐③❡♠♦s q✉❡X é ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❝♦♥tí♥✉❛✳ ◆❡ss❡ tr❛❜❛❧❤♦ ❢♦❝❛♠♦s ❛♣❡♥❛s ❡♠ ✈❛r✐á✈❡✐s ❞✐s❝r❡t❛s✳
❉❡✜♥✐çã♦ ✶✸✳ ❆ ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ X ❡stá ❛ss♦❝✐❛❞♦ ✉♠❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ P ❡s❝r✐t❛ P(X =x) ❡♠ q✉❡ x r❡♣r❡s❡♥t❛ ♦ ✈❛❧♦r q✉❡ ❛ ✈❛r✐á✈❡❧ X ❛ss✉♠❡ ❡ P(X =x) é ❝❤❛♠❛❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✳
❉❡✜♥✐çã♦ ✶✹✳ ❯♠ ✈❡t♦r(X1, X2,· · · , Xn)✱ ♦♥❞❡ ❝❛❞❛ Xi✱i= 1,2,· · · , n, é ✉♠❛ ✈❛r✐á✈❡❧
❛❧❡❛tór✐❛✱ é ❝❤❛♠❛❞♦ ✈❡t♦r ❛❧❡❛tór✐♦✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ s❡ ❝❛❞❛ Xi é ❞✐s❝r❡t❛✱ t❡♠♦s ✉♠
✈❡t♦r ❛❧❡❛tór✐♦ ❞✐s❝r❡t♦✳
❉❡✜♥✐çã♦ ✶✺ ✭❱❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ✐♥❞❡♣❡♥❞❡♥t❡s✮✳ ❆s ✈❛r✐á✈❡✐sX1,· · ·Xn sã♦ ✐♥❞❡♣❡♥✲
❞❡♥t❡s s❡✱ ♣❛r❛ q✉❛❧q✉❡r ❝♦♥❥✉♥t♦ Ai ⊂R, i= 1,· · · , n ✱
P(X1 ∈A1, . . . , Xn∈An) = n
Y
i=1
