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?
Maximal Ergodic Theorem
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probability-theory
dynamical-systems
ergodic-theory
statistical-mechanics
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0Related: http://mathoverflow.net/questions/73248/applications-of-and-motivation-for-von-neumanns-mean-ergodic-theorem – 2012-04-03
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0Excuse me, but I could not understand what this discussion has to do with the maximal ergodic theorem? – 2012-04-03
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0It 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. – 2012-04-04