Kuratowski and Ryll-Nardzewski measurable selection theorem
In mathematics, the Kuratowski–Ryll-Nardzewski measurable selection theorem is a result from measure theory that gives a sufficient condition for a multifunction to have a measurable selection. It is named after the Polish mathematicians Kazimierz Kuratowski and Czesław Ryll-Nardzewski.
Statement of the theorem
Suppose that Ψ is B-weakly measurable, that is, for every open set U of X, we have
Then Ψ has a selection that is B-ℬ(X)-measurable.
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