Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Extensions of measures and the von Neumann selection theorem
HTML articles powered by AMS MathViewer

by Arthur Lubin PDF
Proc. Amer. Math. Soc. 43 (1974), 118-122 Request permission


Let $(X,{B_X})$ be a Blackwell space, where ${B_X}$ is the $\sigma$-algebra of Borel sets. Then if $\sigma$ is a finite measure defined on a countably generated sub-$\sigma$-algebra $B \subset {B_X},\sigma$ can be extended to a Borel measure $\tau$. Equivalently, if $X$ and $Y$ are Blackwell and $f:X \to Y$ is Borel, and $\mu$ is a Borel measure carried on $f(X) \subset Y$, then there exists a Borel measure $\tau$ on $X$ with ${\tau ^f} = \sigma$, where ${\tau ^f}(E) = \tau ({f^{ - 1}}(E))$. We characterize $\{ \tau |{\tau ^f} = \sigma \}$ if $f$ is semischlicht.
  • Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
  • Felix Hausdorff, Set theory, 2nd ed., Chelsea Publishing Co., New York, 1962. Translated from the German by John R. Aumann et al. MR 0141601
  • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
  • N. Lusin, Leçons sur les ensembles analytiques, Hermann, Paris, 1930.
  • Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0205288
  • John von Neumann, On rings of operators. Reduction theory, Ann. of Math. (2) 50 (1949), 401–485. MR 29101, DOI 10.2307/1969463
  • H. L. Royden, Real analysis, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0151555
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A10
  • Retrieve articles in all journals with MSC: 28A10
Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 118-122
  • MSC: Primary 28A10
  • DOI:
  • MathSciNet review: 0330393