1. Existence of tilings

In this case, the hypersurface is either an Einstein manifold (in this case, the Ricci soliton will be called trivial) or an open part of a rotation hypersurface (Theorem 4).

If µ bf (X) = 0 then every measurable subset of X with finite measure has null measure; this implies that the empty family is an essential decomposition for (X, A, µ)... Use the