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Theoretical and experimental aspects of information theory and coding theory. This tag covers but is not limited to following branches: information theory, information geometry, optimal transportation theory, coding theory.

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Continuity of relative entropy with respect to the weak* topology

Now I'll post some sort of an answer, and not just a comment due to the length. Your first question is answered above. For the second one, if you're willing to take the minus inside (take the inverse …
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