Vol. 25, No. 3, 1968

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Invariant measures and Cesàro summability

Howard Jacob Weiner

Vol. 25 (1968), No. 3, 621–629
Abstract

It is known that if T is a one-to-one, measurable, invertible and nonsingular transformation on the unit interval with a σ-finite invariant measure, then its induced transformation T1 on L1 functions f is such that limn→∞1∕n k=1nT1kf(x) exists. In this note, a counterexample is constructed which shows that the converse is false.

Mathematical Subject Classification
Primary: 28.70
Milestones
Received: 6 July 1967
Published: 1 June 1968
Authors
Howard Jacob Weiner