On the integrable selections of certain multifunctions
Let \(F:T\to E\) be a closed valued measurable multifunction from a nonatomic \(\sigma\)-finite measure space \(T\) into a separable Banach space \(E\). Conditions are formulated under which the set of all integrable selections of \(F\) intersects each member of a specially defined family \(\mathfrak V\) of subsets of \(L^1(T,E)\). Among examples of \(\mathfrak V\) there is a family of all closed hyperplanes of \(L^1\). There are indicated many consequences, e.g., concerning relations between convergence of sequences of multifunctions and its selectors, further, properties of Aumann integral, Gâteaux differentiability of the Nemytski operator, etc.
scientific article; zbMATH DE number 898041