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On Baire approximations of normal integrands. (English) Zbl 0685.28001
Let \(D\subset T\times X\), where (T,\({\mathcal T})\) is a measurable space and X a metric space. It is proved that every upper semicontinuous in x and jointly measurable function \(f:D\to \bar R\) is a limit of a decreasing sequence of measurable functions which are continuous in x provided D is Souslin measurable and either T and X are Polish spaces with \({\mathcal T}={\mathcal B}(T)\) or \({\mathcal T}\) is a Souslin family and X is a Souslin space.
Some applications to optimization theory are included. The main result may be viewed as a parametrized version of the famous Baire approximation theorem.
Reviewer: W.Ślȩzak

MSC:
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
54C30 Real-valued functions in general topology
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