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Where can I find the proof of Von Neumann's ergodic theorem? Please, give me references or write names of books where I can find it.

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up vote 3 down vote accepted

The original proof (pdf) is in

J. von Neumann, "Proof of the quasi-ergodic hypothesis" Proc. Nat. Acad. Sci. USA , 18 (1932) pp. 70–82

A simpler proof is due to Halmos, found in

P.R. Halmos, "Lectures on ergodic theory" , Math. Soc. Japan (1956)

I believe this book is a reprinting of those lectures.

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An alternative name for the same result is the mean ergodic theorem and there's a proof in almost every book on ergodic theory. Terry Tao has a blog post on it. –  Martin Jan 24 '13 at 1:25
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If you want more modern books I recommend P. Walters or K. Petersen books on Ergodic Theory.

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