In mathematics, the Kuratowski–Ryll-Nardzewski measurable selection theorem is a result from measure theory that gives a sufficient condition for a set-valued function to have a measurable selection function.
[1][2][3] It is named after the Polish mathematicians Kazimierz Kuratowski and Czesław Ryll-Nardzewski.
[4] Many classical selection results follow from this theorem[5] and it is widely used in mathematical economics and optimal control.
be a Polish space,
the Borel σ-algebra of
a measurable space and
taking values in the set of nonempty closed subsets of
-weakly measurable, that is, for every open subset
[7] This mathematical analysis–related article is a stub.