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Is there any demonstration purely dynamic of the Birkhoff Ergodic Theorem, i.e, without the Maximal Ergodic Theorem??

I ask this question because I never understood the intuition behind The Maximal Ergodic Theorem.

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    There is an [elementary proof](http://dx.doi.org/10.1007/BF02761409) due to Katznelson and Weiss which I found instructive. I do not know if that proof counts as "purely dynamic".2012-12-30
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    I have deleted some unconstructive comments. @HarryPotter: I would advise you to stay on-topic as you are learning your way around this site. "Joke" posts regarding your pseudonym (like the one I just deleted on a different question) will be considered spam.2012-12-30
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    @Martin Could you give the main ideas of Katznelson and Weiss' proof in an answer?2013-02-21

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