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Points of continuity of Kullback-Leibler divergence with respect to weak convergence

What I was wondering is whether there are simple characterisations, or at least sufficient conditions for couple of measures to be points of (sequential) continuity. … In the specific problem I have in mind, I'm particularly interested in continuity with respect to $\nu$: I have a sequence $\nu_n$ weakly converging to $\nu$ and I would want to understand cases depending …
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