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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Extensions of measures and the von Neumann selection theorem
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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.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 118-122
  • MSC: Primary 28A10
  • DOI:
  • MathSciNet review: 0330393