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Characterizations of d -total boundedness for classes of B sources

Strong universal coding is possible for any dass of ergodic sources on a finite alphabet which is totally bounded in the \bar{d} distance. In order to implement this theorem, several necessary and sufficient conditions are given in order for a class of B sources to be \bar{d} -totally bounded. The conditions are applied to several examples. Of independent interest is a result which allows one to model a \bar{d} -totally bounded class of B sources as an encoding of the dass of memoryless sources, where the encoder satisfies a certain continuity property.