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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
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.

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Article copyright: © Copyright 1977 American Mathematical Society