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)

 
 

 

On the existence of invariant measures that behave like area


Author: Stewart Baldwin
Journal: Proc. Amer. Math. Soc. 115 (1992), 89-96
MSC: Primary 58F11; Secondary 28C10, 54H20
DOI: https://doi.org/10.1090/S0002-9939-1992-1112485-1
MathSciNet review: 1112485
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A countably additive measure on a locally compact, separable, metric space $ X$ will be called area-like if points have measure zero, compact sets have finite measure, and nonempty open sets have nonzero measure. Given a homeomorphism $ f$ of $ X$, we examine criteria that guarantee the existence or nonexistence of arealike measures that are invariant under $ f$.


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

  • [BS] Stewart Baldwin and Edward E. Slaminka, On measures preserved by Brouwer homeomorphisms, Topology Proc. 14 (1989), 1-6. MR 1081115 (92a:54034)
  • [GS] L. Garrido and C. Simó, Some ideas about strange attractors, Lecture Notes in Phys., vol. 179, Springer-Verlag, 1982, pp. 1-28. MR 708543 (84j:58076)
  • [KB] N. Kryloff and N. Bogoliouboff, La théorie générale de la mesure dans son application à l'étude des systems dynamique de la mécanique non linéaire, Ann. of Math. (2) 38 (1937), 65-113. MR 1503326
  • [OU] J. C. Oxtoby and S. M. Ulam, Measure preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941), 874-920. MR 0005803 (3:211b)
  • [W] Peter Walters, An introduction to ergodic theory, Springer-Verlag, New York, Heidelberg and Berlin, 1982. MR 648108 (84e:28017)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F11, 28C10, 54H20

Retrieve articles in all journals with MSC: 58F11, 28C10, 54H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1112485-1
Keywords: Invariant measure, area-preserving homeomorphism
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society