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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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