Characterizations ofd-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.