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• W1601488360 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 @a, the base-k expansions of @a, q+@a, and q@a 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." @default.
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• W1601488360 date "2006-01-01" @default.
• W1601488360 modified "2023-09-23" @default.
• W1601488360 title "Finite-State Dimension and Real Arithmetic." @default.
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