Rate Distortion Theory for Sources with Abstract Alphabets and Memory

This paper is devoted to the formulation and proof of an abstract alphabet version of the fundamental theorem of Shannon's rate distortion theory. The validity of the theorem is established for both discrete and continuous parameter information sources satisfying a certain regularity condition intermediate in restrictiveness between ergodicity and weak mixing. For ease of presentation, only single letter fidelity criteria are considered during the main development after which various generalizations are indicated.