Fractional Differentiation in the Self-Affine Case III. The Density of the Cantor Set

DOI10.2307/2159708zbMath0854.60009OpenAlexW4243683327MaRDI QIDQ4032512

Norbert Patzschke, Martina Zähle

Publication date: 1 April 1993

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

Full work available at URL: https://doi.org/10.2307/2159708

zbMATH Keywords

fractional density of the middle-third Cantor measure

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Extreme value theory; extremal stochastic processes (60G70) Length, area, volume, other geometric measure theory (28A75) Random measures (60G57) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Self-similar stochastic processes (60G18) Fractals (28A80)

Related Items (10)

Average densities of the image and zero set of stable processes ⋮ On Bandt's tangential distribution for self-similar measures ⋮ Fractional differentiation in the self-affine case. IV — random measures ⋮ PROGRESS ON ESTIMATION OF FRACTAL DIMENSIONS OF FRACTIONAL CALCULUS OF CONTINUOUS FUNCTIONS ⋮ ON THE FRACTIONAL DERIVATIVE OF A TYPE OF SELF-AFFINE CURVES ⋮ A geometric based connection between fractional calculus and fractal functions ⋮ Fractional Differentiation in the Self‐Affine Case. V ‐ The Local Degree of Differentiability ⋮ Wavelet transforms and order-two densities of fractals ⋮ Symmetry properties of average densities and tangent measure distributions of measures on the line ⋮ The pointwise densities of the Cantor measure

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