Olech’s correction to the proof of his theorem on existence of solutions to differential inclusions

In 1975 Czeslaw Olech published in this journal a theorem on existence of solutions to differential inclusions with right-hand side measurable with respect to the time variable, upper semicontinuous with respect to the state variable and continuous at the arguments at which it is not convex. It occurred that the proof contained errors. This paper relates its correct version with some simplifications.