Bimeasurable functions

Author:
R. Daniel Mauldin

Journal:
Proc. Amer. Math. Soc. **83** (1981), 369-370

MSC:
Primary 54C65; Secondary 04A15, 28C15, 54H05

DOI:
https://doi.org/10.1090/S0002-9939-1981-0624933-4

MathSciNet review:
624933

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be complete, separable metric spaces, a Borel subset of and a Borel measurable map of into . The map is said to be bimeasurable if the image of every Borel subset of is a Borel subset of . R. Purves proved that is bimeasurable if and only if is uncountable is countable. The purpose of this note is to demonstrate how Purves' theorem can be obtained directly from some results concerning parametrization of sets which have been developed in the past few years.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0624933-4

Keywords:
Borel isomorphism,
bimeasurable function

Article copyright:
© Copyright 1981
American Mathematical Society