Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
427314 | Information and Computation | 2007 | 12 Pages |
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.
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