Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A constructive ergodic theorem


Author: J. A. Nuber
Journal: Trans. Amer. Math. Soc. 164 (1972), 115-137
MSC: Primary 28A65; Secondary 02E99
Erratum: Trans. Amer. Math. Soc. 216 (1976), 393.
MathSciNet review: 0291411
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: As discussed by Bishop, Birkhoff's Ergodic Theorem is not constructively valid. In this paper we present an hypothesis which is necessary and sufficient for the constructive almost everywhere convergence of the Césaro averages of the translates of an integrable function by a measure preserving transformation. In addition necessary and sufficient conditions are given for the limit function to be constructively integrable. Also we present a necessary and sufficient condition that the averages converge to a constant function and give an equivalent formulation of this condition for finite measure spaces. Several interesting examples are given which satisfy these conditions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28A65, 02E99

Retrieve articles in all journals with MSC: 28A65, 02E99


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0291411-3
PII: S 0002-9947(1972)0291411-3
Keywords: Birkhoff's Ergodic Theorem, measure preserving transformation, constructive mathematics, almost everywhere convergence, Césaro averages, integrable function
Article copyright: © Copyright 1972 American Mathematical Society