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Additive Families of Low Borel Classes and Borel Measurable Selectors |
Canad. Math. Bull. 54(2011), 180-192
Published:2010-08-03
Printed: Mar 2011
Printed: Mar 2011
- J. Spurný,
- M. Zelený,
Abstract
An important conjecture in the theory of Borel sets in non-separable
metric spaces is whether any point-countable Borel-additive family in
a complete metric space has a $\sigma$-discrete refinement. We confirm the conjecture for
point-countable $\mathbf\Pi_3^0$-additive families, thus generalizing results of
R. W. Hansell and the first author. We apply this result to the
existence of Borel measurable selectors for multivalued mappings of
low Borel complexity, thus answering in the affirmative a particular
version of a question of J. Kaniewski and R. Pol.
| Keywords: | $\sigma$-discrete refinement, Borel-additive family, measurable selection |
| MSC Classifications: |
54H05 - Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 54E35 - Metric spaces, metrizability |