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Some ergodic theorems

Published online by Cambridge University Press:  14 November 2011

Nelson Dunford
Nelson Dunford
Affiliation:
Sarasota, Florida 33577, U.S.A.
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Synopsis

A general ergodic theorem is proved for semi-group operators on B-space X. In particular X may be a Lebesgue space Lp(S, Σ, μ) where (S, Σ, μ) is a positive measure space.

The discussion is based on the theory of semi-groups as developed by Hille [6] and results in the theory of product measures [3]. The reader need only be familiar with the basic concepts of these theories, as all pertinent results used in this note are proved as they are needed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 85 , Issue 1-2 , 1980 , pp. 111 - 118
Copyright
Copyright © Royal Society of Edinburgh 1980

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References

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