In this paper, we propose a quantification of distributions on a set
of strings, in terms of how close to pseudorandom the distribution
is. The quantification is an adaptation of the theory of dimension of
sets of infinite sequences first introduced by Lutz
\cite{Lutz:DISS}.
We show that this definition ... more >>>

We use entropy rates and Schur concavity to prove that, for every integer k >= 2, every nonzero rational number q, and every real number alpha, the base-k expansions of alpha, q+alpha, and q*alpha all have the same finite-state dimension and the same finite-state strong dimension. This extends, and gives ... more >>>