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Transactions of the American Mathematical Society

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Disintegration of measures on compact transformation groups


Author: Russell A. Johnson
Journal: Trans. Amer. Math. Soc. 233 (1977), 249-264
MSC: Primary 28A50
DOI: https://doi.org/10.1090/S0002-9947-1977-0444897-X
MathSciNet review: 0444897
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Abstract: Let G be a compact metrizable group which acts freely on a locally compact Hausdorff space X. Let X, $ \mu $ be a measure on $ X,\pi :X \to X/G \equiv Y$ the projection, $ \nu = \pi (\mu )$. We show that there is a $ \nu$-Lusin-measurable disintegration of $ \mu $ with respect to it. We use this result to prove a structure theorem concerning T-ergodic measures on bitransformation groups (G, X, T) with G metric and X compact. We finish with some remarks concerning the case when G is not metric.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9947-1977-0444897-X
Article copyright: © Copyright 1977 American Mathematical Society

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