In this paper, we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver. We study the mutual information function and some of its analytical properties such as strict concavity and continuity. For this purpose, we use the weak topology and establish necessary and sufficient conditions for strict concavity and continuity of the mutual information based on the weak topology. We then raise the issue of capacity analysis and address necessary and sufficient conditions for the existence, uniqueness, and the expression of capacity-achieving measure.
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