Vol. 103, No. 2, 1982

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Pointwise ergodic theorems in l.c.a. groups

Julius Rubin Blum and J. I. Reich

Vol. 103 (1982), No. 2, 301–306

Let G be a l.c.a. group and {Tg} be a representation of G such that each Tg is a measure-preserving transformation on some probability space ,,P). Let {μn} be a sequence of probability measures on G. We are interested in the a.e. convergence or summability of G f(Tgw)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
Received: 15 September 1980
Published: 1 December 1982
Julius Rubin Blum
J. I. Reich