ИСТИНА

If a stochastic transition kernel, that maps every point from a topological space to the probability measure on a separable metric space, satisfies the Feller property, then the multifunction that maps every point from the given topological space to the topological support of the corresponding probability measure, is lower semicontinuous. Conversely, if the state space is perfectly normal and a multivalued mapping takes non-empty closed values in a Polish space is lower semicontinuous, then, there exist a Feller transition kernel such that for every state the supports of the corresponding probability measure coincide with the value of the given multifunction.