On total boundedness for existence of weakly minimax universal codes (Corresp.)

Stationary processes whose restrictions are totally bounded in variation distance are shown to be equivalent to the class of tight measures when the alphabet is countable. For uncountable alphabets, total boundedness implies tightness, but the reverse implication need not hold, as shown by example. Necessary and sufficient conditions for the class of Gaussian processes to be bounded totally are presented. An application of these results to universal coding for composite sources is considered.