Article ID Journal Published Year Pages File Type
427314 Information and Computation 2007 12 Pages PDF
Abstract

We use entropy rates and Schur concavity to prove that, for every integer k ⩾ 2, every nonzero rational number q, and every real number α, the base-k expansions of α, q + α, and qα 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.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics