Superfractality of the set of incomplete sums of one positive series

DOI10.1007/s11253-019-01594-yzbMath1477.40002OpenAlexW2945790991MaRDI QIDQ2274575

I. O. Savchenko, V. P. Markitan, Mykola V. Pratsiovytyi

Publication date: 20 September 2019

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-019-01594-y

zbMATH Keywords

Hausdorff-Besicovitch dimensioninfinite Bernoulli convolutionincomplete sumsabnormally fractalpositive seriessuperfractality

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Convergence and divergence of series and sequences (40A05) Fractals (28A80)

Related Items (2)

Fractal functions of exponential type that is generated by the \(Q_2^*\)-representation of argument ⋮ Superpositions of functions with fractal properties

Cites Work

• On the random series \(\sum\pm\lambda^ n\) (an Erdös problem)
• The distributions of random incomplete sums of a series with positive terms satisfying the property of non-linear homogeneity
• Absolutely convergent series and Hausdorff measure
• Jessen–Wintner type random variables and fractal properties of their distributions
• On a paper of Guthrie and Nymann on subsums of infinite series
• Fractal properties of some Bernoulli convolutions
• Hausdorff measure of linear sets
• The topological structure of the set of subsums of an infinite series
• Sets of Fractional Dimensions which Occur in Some Problems of Number Theory
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