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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The nonexistence of certain invariant measures
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by Paul Erdős and R. Daniel Mauldin PDF
Proc. Amer. Math. Soc. 59 (1976), 321-322 Request permission

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
  • 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
  • J. C. Oxtoby, Math Reviews 49 #10861.
  • A. Iwanik, On infinite complete algebras, Colloq. Math. 29 (1974), 195–199, 307. MR 335397, DOI 10.4064/cm-29-2-195-199
  • S. M. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930), 141-150.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 321-322
  • MSC: Primary 28A70
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0412390-0
  • MathSciNet review: 0412390