TR06-038 Authors: David Doty, Jack H. Lutz, Satyadev Nandakumar, Satyadev Nandakumar

Publication: 17th March 2006 05:22

Downloads: 907

Keywords:

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 a new proof of, Wall's 1949 theorem stating that the sum or product of a nonzero rational number and a Borel normal number is always Borel normal.