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Scorza Dragoni type theorems. (English) Zbl 0744.28011
A Scorza-Dragoni type result verifies that if $$f(t,x)$$ is a mapping on $$T\times X$$, measurable in $$t$$, and has a continuity property in $$x$$, then the restriction of $$f$$ to a set $$K\times K$$ has the same continuity property, with $$K\subset T$$ such that the measure of $$T\backslash K$$ is arbitrarily small. Here $$T$$ is a topological space with a measure on it, and $$X$$ is a topological space. The paper establishes Scorza-Dragoni type results under quite relaxed topological conditions on $$T$$, $$X$$ and the range of $$f$$, and for various continuity and semi-continuity properties on $$f$$, which may also be a multifunction. Baire versions of the results are also provided.

MSC:
 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections 54C60 Set-valued maps in general topology 54C65 Selections in general topology
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