Differential inclusions with mean derivatives, having aspherical right-hand sides

Abstract

On flat n-dimensional torus we study stochastic differential inclusions with mean derivatives,
for which the right-hand sides have, generally speaking, not convex (aspherical) values.
A subclass of such inclusions is distinguished for which there exists a sequence of $\varepsilon$-approximations,
converging point-wise to a Borel measurable selector. On this base a solution existence
theorem is obtained.