Riesz products, Hausdorff dimension and normal numbers

DOI10.1017/S0305004100066895zbMath0625.10043OpenAlexW2026033053MaRDI QIDQ3027104

Gavin Brown, William Moran, Charles E. M. Pearce

Publication date: 1987

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100066895

zbMATH Keywords

Hausdorff dimensionnormal numbersRiesz product measuresmultiplicatively independent sets

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16)

Related Items (13)

Dimension and entropy of a non-ergodic Markovian process and its relation to Rademacher Riesz products ⋮ The discrimination theorem for normality to non-integer bases ⋮ Equidistribution for measures defined by digit restrictions ⋮ Equidistribution from fractal measures ⋮ An inequality, with applications to Cantor measures and normal numbers ⋮ On Hausdorff dimension of certain Riesz product in local fields ⋮ Hausdorff dimension of measures with arithmetically restricted spectrum ⋮ Schmidt's conjecture on normality for commuting matrices ⋮ Pointwise normality and Fourier decay for self-conformal measures ⋮ On a generalized entropy's formula ⋮ Some properties of Riesz products on the ring of \(p\)-adic integers ⋮ On the Hausdorff dimension of Rademacher Riesz products ⋮ A Fourier series formula for energy of measures with applications to Riesz products

Cites Work

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• On normal numbers
• The Hausdorff dimension of a set of normal numbers
• Étude de quelques propriétés des produits de Riesz
• Riesz Products and Normal Numbers
• A Gap Theorem
• Sets of Fractional Dimensions which Occur in Some Problems of Number Theory

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