A causal rate distortion function with a general fidelity criterion is
formulated on abstract alphabets and a coding theorem is derived. Existence of
the minimizing kernel is shown using the topology of weak convergence of
probability measures. The optimal reconstruction kernel is derived, which is
causal, and certain properties of the causal rate distortion function are
presented.Comment: 5 pages, Submitted to Internation Symposium on Information
Theory(ISIT) 201