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)



The nonexistence of universal invariant measures

Authors: C. Ryll-Nardzewski and R. Telgársky
Journal: Proc. Amer. Math. Soc. 69 (1978), 240-242
MSC: Primary 28A70
MathSciNet review: 0466494
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for arbitrary nontrivial $ \sigma $-finite measure defined on all subsets of a group there are at most countably many left translations of that measure that are mutually equivalent in the sense of the absolute continuity.

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

  • [1] W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Grundlehren math. Wiss., Bd. 211, Springer-Verlag, Berlin, 1974. MR 0396267 (53:135)
  • [2] N. Dunford and J. Schwartz, Linear operators, Vol. I, Interscience, New York, 1958.
  • [3] P. Erdös and R. D. Mauldin, The nonexistence of certain invariant measures, Proc. Amer. Math. Soc. 59 (1976), 321-322. MR 0412390 (54:516)
  • [4] F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Reinhold, New York, 1969. MR 0251549 (40:4776)
  • [5] S. M. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930), 141-150.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A70

Retrieve articles in all journals with MSC: 28A70

Additional Information

Keywords: Left-invariant measure, measurable cardinal
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society