In this paper we consider differential inclusions in a separable Banach space and we show that when the orientor field satisfies the Caratheodory conditions and is Lipschitzean with respect to a Kamke function w(t, x) in the state variable, then the set of solutions of the nonconvex problem is dense in the {C_x}(T)-topology in the set of solutions of the convexified problem.
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