On the Strong Invariance Property for Non-Lipschitz Dynamics
  We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the multifunction, we assume a feedback realization condition that can in particular be satisfied for measurable dynamics that are neither upper nor lower semicontinuous. 
Mikhail Krastanov, Michael Malisoff, Peter Wolenski