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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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Point-finite Borel-additive families are of bounded class
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by R. W. Hansell PDF
Proc. Amer. Math. Soc. 83 (1981), 375-378 Request permission

Abstract:

We prove the following theorem, which answers a question originally raised by J. Kaniewski and R. Pol: Theorem. If $\mathfrak {X}$ is a point-finite family of subsets of a metric space $X$ such that the union of every subfamily is a Borel set of $X$, then there exists a fixed countable ordinal $\alpha$ such that each member of $\mathfrak {X}$ is a Borel set of class $\alpha$ in $X$. The proof is given in the general setting of abstract measurable spaces. An application is made to the study of measurable selectors for compact-valued mappings and to the Borel measurability of graphs.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 375-378
  • MSC: Primary 54H05; Secondary 04A15
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0624935-8
  • MathSciNet review: 624935