Disintegration of measures on compact transformation groups
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 by Russell A. Johnson PDF
 Trans. Amer. Math. Soc. 233 (1977), 249264 Request permission
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 $\nu$Lusinmeasurable disintegration of $\mu$ with respect to it. We use this result to prove a structure theorem concerning Tergodic 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

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Additional Information
 © Copyright 1977 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 233 (1977), 249264
 MSC: Primary 28A50
 DOI: https://doi.org/10.1090/S0002994719770444897X
 MathSciNet review: 0444897