대한수학회보 (Bulletin of the Korean Mathematical Society)
- 제33권1호
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- Pages.57-64
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- 1996
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
Mean ergodic theorem and multiplicative cocycles
- Choe, Geon H. (Department of Mathematics, Korea Advanced Institute of Science and Technology)
- 발행 : 1996.02.01
초록
Let $(X, B, \mu)$ be a probability space. Then we say $\tau : X \to X$ is a measure-preserving transformation if $\mu(\tau^{-1} E) = \mu(E)$. and we call it an ergodic transformation if $\mu(\tau^{-1}E\DeltaE) = 0$ for a measurable subset E implies $\mu(E) = 0$. An equivalent definition is that constant functions are the only $\tau$-invariant functions.