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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The nonexistence of certain invariant measures


Authors: Paul Erdős and R. Daniel Mauldin
Journal: Proc. Amer. Math. Soc. 59 (1976), 321-322
MSC: Primary 28A70
MathSciNet review: 0412390
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Abstract: It is shown that there does not exist an uncountable group $ G$ and a nontrivial, $ \sigma $-finite, countably additive measure defined on all subsets of $ G$ which is left-invariant.


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

  • [1] Frank Terpe, Zur Existenz maximaler translationsgleicher Integrale, Theory of sets and topology (in honour of Felix Hausdorff, 1868–1942), VEB Deutsch. Verlag Wissensch., Berlin, 1972, pp. 495–502 (German). MR 0346135 (49 #10861)
  • [2] J. C. Oxtoby, Math Reviews 49 #10861.
  • [3] A. Iwanik, On infinite complete algebras, Colloq. Math. 29 (1974), 195–199, 307. MR 0335397 (49 #179)
  • [4] S. M. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930), 141-150.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0412390-0
PII: S 0002-9939(1976)0412390-0
Keywords: Left-invariant measure, measurable cardinal
Article copyright: © Copyright 1976 American Mathematical Society