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Proceedings of the American Mathematical Society

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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?)

  • 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
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  • A. Iwanik, On infinite complete algebras, Colloq. Math. 29 (1974), 195–199, 307. MR 335397, DOI
  • S. M. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930), 141-150.

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Keywords: Left-invariant measure, measurable cardinal
Article copyright: © Copyright 1976 American Mathematical Society