Measure differential inclusions through selection principles in the space of regulated functions (Q1790525)

Let \(F\) be a multifunction defined on a unit interval \([0, 1]\) witch convex closed values in a Banach space \(Y\). If \(F\) has nonempty one-sided limits \(F(t-)\), \(F(t+)\) for each \(t\) (with respect to the Hausdorff distance), then \(F\) has a regulated selection. Several theorems of this kind (concerning multifunctions lsc outside an almost countable set of arguments, multifunctions of bounded variation etc.) are proved. Applications to measure differential inclusions, relationships with Kurzweil-Stieltjes integrals are mentioned and some counterexamples are provided.