The validity space of Dunford-Schwartz pointwise ergodic theorem

摘要

We show that if a sigma-finite infinite measure space (Omega, mu) is quasi-non-atomic, then the Dunford Schwartz pointwise ergodic theorem holds for f is an element of L-1(Omega) L-infinity(Omega) if and only if mu{|f| = lambda} infinity for all lambda 0. (C) 2018 Elsevier Inc. All rights reserved.