• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.57-64
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• 1996

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.

• Journal of the Korean Mathematical Society
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• v.9 no.1
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• pp.45-48
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• 1972