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Dimensions of non-differentiability points of Cantor functions

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Yao Y., Zhang Y., Li W.

Studia Mathematica

2009

tom 195

nr 2

113-125

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 $h_{i}(x) = a_{i}x + b_{i}$, 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 $p_{i} > a_{i}$, 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.

Ograniczanie wyników

1 Studia Mathematica

1 Li W.

1 Yao Y.

1 Zhang Y.

1 2009

Wyniki wyszukiwania

Dimensions of non-differentiability points of Cantor functions