Convergence of averages of point transformations
Mustafa A. Akcoglu, Andrés del Junco · Proceedings of the American Mathematical Society · 1975
Let (X, J, p) be a finite measure space. An invertible transformationProposition.// r is an ergodic automorphism of a probability space (X, 3", p), then there is a set E such that there is a set B of positive measure on which X .a.yF(r~'x)fails to converge.