  We prove the existence of codebooks for d-semifaithful lossy compression that
are simultaneously universal with respect to both the class of finite-alphabet
memoryless sources and the class of all bounded additive distortion measures.
By applying independent random selection of the codewords according to a
mixture of all memoryless sources, we achieve redundancy rates that are within
O(log n/n) close to the empirical rate-distortion function of every given
source vector with respect to every bounded distortion measure. As outlined in
the last section, the principal ideas can also be extended significantly beyond
the class of memoryless sources, namely, to the setting of individual sequences
encoded by finite-state machines.
