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Non-differentiability points of Cantor functions

✍ Scribed by Wenxia Li

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
176 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let the Cantor set C in ℝ be defined by C = ∪^r^ ~j =0~ h~j~ (C) with a disjoint union, where the h~j~ 's are similitude mappings with ratios 0 < a~j~ < 1. Let μ be the self‐similar Borel probability measure on C corresponding to the probability vector (p ~0~, p ~1~, …, p~r~). Let S be the set of points at which the probability distribution function F (x) of μ has no derivative, finite or infinite. For the case where p~i~ > a~i~ we determine the packing and box dimensions of S and give an approach to calculate the Hausdorff dimension of S. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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