On A Generalized Entropy’s Formula
Copyright policy )On A Generalized Entropy’s Formula
The authors consider measures \(\mu\) being generalized Rademacher-Riesz products. Using the properties of such products and using Frostman's lemma, they find the Hausdorff dimension of a Borel subset of [0,1] of positive \(\mu\)-measure. Thereby they generalize \textit{H. G. Egglestone}'s result [Q. J. Math., Oxf. II. Ser. 20, 31-36 (1949; Zbl 0031.20801)].
- University of Cyprus Cyprus
- Aristotle University of Thessaloniki Greece
Borel subset, Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc., positive Rademacher-Riesz product measure, Metric theory of other algorithms and expansions; measure and Hausdorff dimension, Hausdorff dimension, uniform distribution mod 1, Eggleston-type formula, normal numbers
Borel subset, Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc., positive Rademacher-Riesz product measure, Metric theory of other algorithms and expansions; measure and Hausdorff dimension, Hausdorff dimension, uniform distribution mod 1, Eggleston-type formula, normal numbers
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