Mixing Conditions and Their Characterisations

Part of the Texts and Readings in Mathematics book series (volume 6)


We have seen that a measure preserving automorphism σ on a probability space (X, Ɓ, m) is ergodic if and only if for all A, BƁ,
$$\frac{1}{n}\sum\limits_{k = 0}^{n - 1} {m\left( {A \cap {\sigma ^k}B} \right) \to m\left( A \right)\;\cdot\;m\left( B \right)} \;as\;n \to \infty$$
. Two properties stronger than ergodieity discovered by Koopman and von Neumann [2] will now be discussed.


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© Hindustan Book Agency 2013

Authors and Affiliations

  1. 1.University of MumbaiIndia

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