A short proof and generalization of a measure theoretic disjointization lemma
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- by Joseph Kupka PDF
- Proc. Amer. Math. Soc. 45 (1974), 70-72 Request permission
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
- Heinz Bachmann, Transfinite Zahlen, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 1, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (German). MR 0071481
- Haskell P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13–36. MR 270122, DOI 10.4064/sm-37-1-13-36 W. Sierpiński, Cardinal and ordinal numbers, 2nd rev. ed., Monografie Mat., vol. 34, PWN, Warsaw, 1965. MR 33 #2549.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 70-72
- MSC: Primary 28A10; Secondary 46B99
- DOI: https://doi.org/10.1090/S0002-9939-1974-0342666-5
- MathSciNet review: 0342666