Pointwise ergodic theorems in l.c.a. groups

Julius Rubin Blum and J. I. Reich

Vol. 103 (1982), No. 2, 301–306

DOI: 10.2140/pjm.1982.103.301

Abstract

Let G be a l.c.a. group and {T_g} be a representation of G such that each T_g is a measure-preserving transformation on some probability space (Ω,ℱ,P). Let {μ_n} be a sequence of probability measures on G. We are interested in the a.e. convergence or summability of ∫ _G f(T_gw)dμ_n(g), for f ∈ L₁(Ω). Some examples and counterexamples are given, and some partial results are obtained.

Mathematical Subject Classification 2000

Primary: 28D05

Secondary: 22D40, 47A35

Milestones

Received: 15 September 1980

Published: 1 December 1982