Parametrizations of Borel sets with large sections. (English) Zbl 0565.54016
The main result (Theorem 1) is the existence of a Borel parametrization of a Borel subset A of \(X\times Y\) for X a separable metric space and Y a Polish space under assumptions that sections of A over points of X are large in terms of some \(\sigma\)-ideals and projections of Borel subsets of A with large sections are Borel measurable in X. Theorem 1 unifies an essential part of several parametrization theorems proved earlier by Mauldin, or Mauldin and Srivastava, respectively. Moreover, the proof made it possible to exclude the assumption of completeness of X. (One should notice that the measurability of f in Theorem 3(III) is omitted by mistake.)
Reviewer: P.Holicky
MSC:
| 54H05 | Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) |
| 28B20 | Set-valued set functions and measures; integration of set-valued functions; measurable selections |
| 03E15 | Descriptive set theory |
| 54C65 | Selections in general topology |
References:
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