Vol. 25, No. 3, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
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