Point-finite Borel-additive families are of bounded class

Author:
R. W. Hansell

Journal:
Proc. Amer. Math. Soc. **83** (1981), 375-378

MSC:
Primary 54H05; Secondary 04A15

MathSciNet review:
624935

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the following theorem, which answers a question originally raised by J. Kaniewski and R. Pol:

Theorem. *If* *is a point-finite family of subsets of a metric space* *such that the union of every subfamily is a Borel set of* , *then there exists a fixed countable ordinal* *such that each member of* *is a Borel set of class* *in* .

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

DOI:
https://doi.org/10.1090/S0002-9939-1981-0624935-8

Keywords:
Borel-additive family,
point-finite family,
Borel classifications,
measurable selectors

Article copyright:
© Copyright 1981
American Mathematical Society