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A Probabilistic Proof of Ergodic Decomposition

Klaus Schmidt
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 40, No. 1 (Jan., 1978), pp. 10-18
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25050129
Page Count: 9
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A Probabilistic Proof of Ergodic Decomposition
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Abstract

Let T be an automorphism of a probability space (X, ${\cal S}$, μ), where μ is quasi-invariant under T. The ergodic decomposition theorem states that the measure μ can be uniquely decomposed into a family of quasi-invariant and ergodic measures for T. In this paper we prove this result using only basic measure theoretic and probabilistic methods, and obtain further information on the properties of such a decomposition.

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