Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] N. Bourbaki, Eléments de mathématique. Intégration, Fasc. XIII, XXI, XXV, 2nd ed., Livre VI, Chaps. 1-4, 5, 6, Actualités Sci. Indust., nos. 1175, 1244, 1281, Hermann, Paris, 1965, 1956, 1959. MR 36 #2763; 18, 881; 23 #A2033.
  • [2] G. Edgar, Disintegration of measures and the vector-valued Radon-Nikodym theorem (pre-print).
  • [3] Robert Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York, 1969. MR 0267561 (42 #2463)
  • [4] Steven A. Gaal, Linear analysis and representation theory, Springer-Verlag, New York-Heidelberg, 1973. Die Grundlehren der mathematischen Wissenschaften, Band 198. MR 0447465 (56 #5777)
  • [5] A. Ionescu Tulcea and C. Ionescu Tulcea, On the existence of a lifting commuting with the left translations of an arbitrary locally compact group, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Univ. California Press, Berkeley, Calif., 1967, pp. 63–97. MR 0212122 (35 #2997)
  • [6] A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York Inc., New York, 1969. MR 0276438 (43 #2185)
  • [7] R. Johnson, Topological and measure-theoretic properties of compact transformation groups with free action, Dissertation, Univ. of Minnesota, 1975.
  • [8] Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104 (17,383b)
  • [9] H. B. Keynes and D. Newton, The structure of ergodic measures for compact group extensions, Israel J. Math. 18 (1974), 363–389. MR 0369660 (51 #5892)
  • [10] William Parry, Compact abelian group extensions of discrete dynamical systems, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 95–113. MR 0260976 (41 #5596)
  • [11] Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470 (33 #1690)
  • [12] E. Rauch, Desintegration von Massen und Zuständen, Dissertation, Erlangen, 1974.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28A50

Retrieve articles in all journals with MSC: 28A50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0444897-X
PII: S 0002-9947(1977)0444897-X
Article copyright: © Copyright 1977 American Mathematical Society