A generalized typicality for abstract alphabets

A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, and some basic properties, which closely resemble those of strong typical sets for finite alphabet, are stated. Using that, both the packing lemma and the covering lemma can be proved, so many basic tools for achievability proofs for various multi-terminal coding problems only used for the finite alphabet case, are now available also in the general case. Hence, lots of finite alphabet results can be transferred to the general case, without significantly altering the proofs; for instance, without any quantization procedure.