Causal Rate Distortion Function on Abstract Alphabets: Optimal   Reconstruction and Properties
  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. 
Photios A. Stavrou, Charalambos D. Charalambous and Christos K.   Kourtellaris
cs.IT math.FA math.IT math.PR