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.References
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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