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Riemann-measurable selections. (English) Zbl 0851.54021
Summary: Let $$X$$ be a Polish space equipped with a $$\sigma$$-finite regular Borel measure $$\mu$$. If $$E$$ is a metric space and $$F$$ a set-valued function: $$X\to 2^E$$ with complete values, and if $$F$$ is lower semicontinuous at almost all points of $$X$$, we prove that there exists a Riemann-measurable selection $$s$$ of $$F$$.

##### MSC:
 54C65 Selections in general topology 54C60 Set-valued maps in general topology
##### Keywords:
Riemann-measurable selection
Full Text:
##### References:
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