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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Disintegration of measures on compact transformation groups
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by Russell A. Johnson PDF
Trans. Amer. Math. Soc. 233 (1977), 249-264 Request permission


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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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 233 (1977), 249-264
  • MSC: Primary 28A50
  • DOI:
  • MathSciNet review: 0444897