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A short proof and generalization of a measure theoretic disjointization lemma


Author: Joseph Kupka
Journal: Proc. Amer. Math. Soc. 45 (1974), 70-72
MSC: Primary 28A10; Secondary 46B99
MathSciNet review: 0342666
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Abstract: This paper presents general conditions under which a subfamily may be selected from an infinite family of nonnegative, finitely additive measures such that this subfamily has the same cardinality as the original family, and such that the members of this subfamily are, in a certain sense, dis jointly supported. The generalized continuum hypothesis is required for the general result, but not for a special case of this result which had previously been obtained by Rosenthal, and for which the present techniques yield a much shorter proof.


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

  • [1] Heinz Bachmann, Transfinite Zahlen, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 1, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (German). MR 0071481
  • [2] Haskell P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13–36. MR 0270122
  • [3] W. Sierpiński, Cardinal and ordinal numbers, 2nd rev. ed., Monografie Mat., vol. 34, PWN, Warsaw, 1965. MR 33 #2549.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0342666-5
Keywords: Finitely additive measures, cardinality
Article copyright: © Copyright 1974 American Mathematical Society