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Does the maximal ergodic theorem have any dynamical or qualitative interpretations, or is it just a custom-made theorem to leave the demonstration of the Birkhoff ergodic theorem more elegant?

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Related: mathoverflow.net/questions/73248/… –  Quinn Culver Apr 3 '12 at 13:30
Excuse me, but I could not understand what this discussion has to do with the maximal ergodic theorem? –  user27456 Apr 3 '12 at 20:29
It might not. But it gives, in particular, a "qualitative interpretation" of the mean ergodic theorem; specifically, Von Neumann thought the Mean ET was sufficient for a certain physical scenario. Since the two theorems are related (though to what extent I know not), there might be some way to understand a physical interpretation of the Maximal ET. –  Quinn Culver Apr 4 '12 at 3:39
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The answer apparently is yes, a theorem is technical, the deltalhes are given in the article below:


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