On the sum of digits of real numbers represented in the dyadic system. (On sets of fractional dimensions II.)

From MaRDI portal
Publication:1840079

DOI10.1007/BF01448030zbMath0009.39503OpenAlexW145774204MaRDI QIDQ1840079

A. S. Besicovitch

Publication date: 1934

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/159725



Related Items

On new fractal phenomena connected with infinite linear IFS, Unnamed Item, Spectrum of weighted Birkhoff average, Individual behaviors of oriented walks., Upper and lower fast Khintchine spectra in continued fractions, On the multifractal spectrum of weighted Birkhoff averages, Hausdorff Dimension and Nonlinear Relations Between Frequencies of Digits, Metric properties about Banach averages and super simply normal numbers, The dimensions of individual strings and sequences, On upper and lower fast Khintchine spectra of continued fractions, On Hausdorff and topological dimensions of the Kolmogorov complexity of the real line, Multifractal analysis on the level sets described by moving averages, A NONCONVENTIONAL STRONG LAW OF LARGE NUMBERS AND FRACTAL DIMENSIONS OF SOME MULTIPLE RECURRENCE SETS, Hausdorff and packing dimensions of non-normal tuples of numbers: non-linearity and divergence points, Dimensions of random covering sets in Riemann manifolds, Dimensions of modified Besicovitch-Eggleston sets, Dimensions of slices through the Sierpiński gasket, Absolutely convergent series and Hausdorff measure, On fractal faithfulness and fine fractal properties of random variables with independent \(Q^*\)-digits, Dimension spectrum for a nonconventional ergodic average, Dimensions of modified Besicovitch subsets of Moran fractal, A remark on exceptional sets in Erdös-Rényi limit theorem, On the distribution of digits in dyadic expansions, Some results on homeomorphisms between fractal supports of copulas, Hausdorff dimension of the set of almost convergent sequences, On the intersections of the Besicovitch sets and the Erdös-Rényi sets, Unnamed Item, Hausdorff dimension of sets defined by almost convergent binary expansion sequences, Effective Dimensions and Relative Frequencies, Asymptotic behavior of distribution of frequencies of digits, The graph and range singularity spectra of \(b\)-adic independent cascade functions, Hausdorff dimension of limsup sets of random rectangles in products of regular spaces, Infinite non-conformal iterated function systems, Effective dimensions and relative frequencies, Lyapunov exponents for products of matrices and multifractal analysis. I: Positive matrices, On the Hausdorff dimension of fractals given by certain expansions of real numbers, Cubic relations between frequencies of digits and Hausdorff dimension, Digit frequencies of beta-expansions, Ubiquity and large intersections properties under digit frequencies constraints, Fractal Dimensions and Random Transformations, Hausdorff dimension of limsup sets of rectangles in the Heisenberg group, Birkhoff spectrum for piecewise monotone interval maps, A practical method to experimentally evaluate the Hausdorff dimension: An alternative phase-transition-based methodology, Multifractal decompositions of Moran fractals, Fractal dimension versus process complexity, On the range of simple symmetric random walks on the line, Dimensions of subsets of Cantor-type sets, Examples on Harmonic Measure and Normal Numbers, Singularity of self-similar measures with respect to Hausdorff measures, Ubiquitous systems and metric number theory, Dimensions of weighted Besicovitch sets, Ergodic limits on the conformal repellers, On the multifractal analysis of measures, On the Hausdorff dimension of generalized Besicovitch-Eggleston sets of \(d\)-tuples of numbers, Frequency of a digit in the representation of a number and the asymptotic mean value of the digits, Applications of multifractal divergence points to some sets of \(d\)-tuples of numbers defined by their \(N\)-adic expansion, On the Lyapunov spectrum for rational maps, Frequencies of digits under trigonometric perturbations, Exceptional digit frequencies and expansions in non-integer bases, Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches, The Hausdorff dimension of a class of fractals, which are determined by the distribution of dyadic digits, Hausdorff dimensions of level sets related to moving digit means, Oscillation of functions in the Hölder class, Orthogonal exponentials, translations, and Bohr completions, A NOTE ON THE INTERSECTIONS OF THE BESICOVITCH SETS AND ERDŐS–RÉNYI SETS, Dimension of homogeneous rational self-similar measures with overlaps, Numbers with simply normal β-expansions, Graphen reeller Funktionen. (Graphs of real functions), Über Hausdorffsche Dimensionen von Mengen, die durch Zifferneigenschaften charakterisiert sind. VI, Die Dimensionsfunktion von Punktmengen, The Mass Transference Principle: Ten years on, On the intersections of exceptional sets in Borel’s normal number theorem and Erdös–Rényi limit theorem, Multifractal analysis for expanding interval maps with infinitely many branches, Topological and fractal properties of real numbers which are not normal, Dimension, entropy and Lyapunov exponents, Hausdorff dimension of frequency sets in beta-expansions, Unexpected distribution phenomenon resulting from Cantor series expansions, On the snow flake domain, Dimensional explanation of capacity and ambiguity in information theory, The Hausdorff and packing measure of some digital expansions