Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Measures invariant under local homeomorphisms

Author: David Ross
Journal: Proc. Amer. Math. Soc. 102 (1988), 901-905
MSC: Primary 28C10; Secondary 03H05, 28E05
MathSciNet review: 934864
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose $ X$ is a compact Hausdorff space, and $ G$ is a set of local homeomorphisms of $ X$; sufficient conditions are given for the existence of a $ G$-invariant Borel probability measure $ P$ on $ X$. The result generalizes theorems of Mycielski and Steinlage. The proof is an application of the "Loeb measure" construction from nonstandard analysis.

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

  • [1] Nigel J. Cutland, Nonstandard measure theory and its applications, Bull. London Math. Soc. 15 (1983), no. 6, 529–589. MR 720746, 10.1112/blms/15.6.529
  • [2] R. Daniel Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, Mass., 1981. Mathematics from the Scottish Café; Including selected papers presented at the Scottish Book Conference held at North Texas State University, Denton, Tex., May 1979. MR 666400
  • [3] Jan Mycielski, Remarks on invariant measures in metric spaces, Colloq. Math. 32 (1974), 105–112, 150. MR 0361005
  • [4] Leopoldo Nachbin, The Haar integral, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. MR 0175995
  • [5] D. Ross, Measurable transformations and saturated models of analysis, Ph.D. Thesis, University of Wisconsin, 1983.
  • [6] R. C. Steinlage, On Haar measure in locally compact 𝑇₂ spaces, Amer. J. Math. 97 (1975), 291–307. MR 0369665
  • [7] K. D. Stroyan and José Manuel Bayod, Foundations of infinitesimal stochastic analysis, Studies in Logic and the Foundations of Mathematics, vol. 119, North-Holland Publishing Co., Amsterdam, 1986. MR 849100

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28C10, 03H05, 28E05

Retrieve articles in all journals with MSC: 28C10, 03H05, 28E05

Additional Information

Article copyright: © Copyright 1988 American Mathematical Society