The minimax redundancy is a lower bound for most sources

The capacity of the channel induced by a given class of sources is well known to be an attainable lower bound on the redundancy of universal codes w.r.t this class, both in the minimax sense and in the Bayesian (maximin) sense. The authors main contribution is a relatively simple proof that the capacity is essentially a lower bound also in a stronger sense, that is, for “most” sources in the class. This result extends Rissanen´s (1984) lower bound for parametric families. Finally, the authors demonstrate the applicability of this result in several examples