A simple proof of the ergodic theorem using nonstandard analysis |
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Authors: | Teturo Kamae |
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Institution: | (1) Department of Mathematics, Osaka City University, Sugimoto-cho, Osaka, Japan |
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Abstract: | A simple proof of the individual ergodic theorem is given. The essential tool is the nonstandard measure theory developed
by P. Loeb. Any dynamical system on an abstract Lebesgue space can be represented as a factor of a “cyclic” system with a
hyperfinite cycle. The ergodic theorem for such a “cyclic” system is almost trivial because of its simple structure. The general
case follows from this special case. |
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Keywords: | |
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