  Capacity analysis for channels with side information at the receiver has been
an active area of interest. This problem is well investigated for the case of
finite alphabet channels. However, the results are not easily generalizable to
the case of continuous alphabet channels due to analytic difficulties inherent
with continuous alphabets. In the first part of this two-part paper, we address
an analytical framework for capacity analysis of continuous alphabet channels
with side information at the receiver. For this purpose, we establish novel
necessary and sufficient conditions for weak* continuity and strict concavity
of the mutual information. These conditions are used in investigating the
existence and uniqueness of the capacity-achieving measures. Furthermore, we
derive necessary and sufficient conditions that characterize the capacity value
and the capacity-achieving measure for continuous alphabet channels with side
information at the receiver.
