Another proof for the equivalence between invariance of closed sets with respect to stochastic and deterministic systems

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We provide a short and elementary proof for the recently proved result by G. da Prato and H. Frankowska that -- under minimal assumptions -- a closed set is invariant with respect to a stochastic control system if and only if it is invariant with respect to the (associated) deterministic control system.
revised version for publication in Bulletin des Sciences Mathematiques

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