For a probability vector (p₀,p₁) there exists a corresponding self-similar Borel probability measure μ supported on the Cantor set C (with the strong separation property) in ℝ generated by a contractive similitude , i = 0,1. Let S denote the set of points of C at which the probability distribution function F(x) of μ has no derivative, finite or infinite. The Hausdorff and packing dimensions of S have been found by several authors for the case that , i = 0,1. However, when p₀ < a₀ (or equivalently p₁ < a₁) the structure of S changes significantly and the previous approaches fail to be effective any more. The present paper is devoted to determining the Hausdorff and packing dimensions of S for the case p₀ < a₀.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-2,
author = {Yuanyuan Yao and Yunxiu Zhang and Wenxia Li},
title = {Dimensions of non-differentiability points of Cantor functions},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {113-125},
zbl = {1189.28008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-2}
}
Yuanyuan Yao; Yunxiu Zhang; Wenxia Li. Dimensions of non-differentiability points of Cantor functions. Studia Mathematica, Tome 192 (2009) pp. 113-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-2/