A remark on a lemma from Filippov's article on differential inclusions

The Filippov's article discusses a possible definition of the solution of differential equation with discontinuous right-hand side. The lemma on the structure of the set defining differential inclusion given by Filippov implies an equivalent solution definition, which allows us to expand possible domains and codomains of the function, that is in the right-hand side of the equation.
In this paper we find a generalization of this lemma to the case of general topologic and measure spaces. Proofs of corresponding theorems are given here.