A descriptive characterization of Ergodic systems

Nadkarni, M. G. (1983) A descriptive characterization of Ergodic systems Sankhya: The Indian Journal of Statistics, 45 (3). pp. 271-287. ISSN 0972-7671

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Given a Borel structure (X, β) and a T : X → X a Borel automorphism, we give a necessary and sufficient condition (in terms of existence of a suitable σ-ideal for there to exist on β a continuous probability measure which is invariant under T and with respect to which T is ergodic. Some related questions are discussed.

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