Points of infinite derivative of Cantor functions

Wenxia Li

doi:10.14321/realanalexch.32.1.0087

Points of infinite derivative of Cantor functions

Wenxia Li

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider self-similar Borel probability measures μ on a self-similar set E with strong separation property. We prove that for any such measure μ the derivative of its distribution function F(x) is infinite for μ-a.e. x ∈ E, and so the set of points at which F(x) has no derivative, finite or infinite is of μ-zero.

Original language	English
Pages (from-to)	87-96
Number of pages	10
Journal	Real Analysis Exchange
Volume	32
Issue number	1
DOIs	https://doi.org/10.14321/realanalexch.32.1.0087
State	Published - 2007

Keywords

Cantor functions
Non-differentiability
Self-similar measures
Self-similar sets

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10.14321/realanalexch.32.1.0087

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title = "Points of infinite derivative of Cantor functions",

abstract = "We consider self-similar Borel probability measures μ on a self-similar set E with strong separation property. We prove that for any such measure μ the derivative of its distribution function F(x) is infinite for μ-a.e. x ∈ E, and so the set of points at which F(x) has no derivative, finite or infinite is of μ-zero.",

keywords = "Cantor functions, Non-differentiability, Self-similar measures, Self-similar sets",

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year = "2007",

doi = "10.14321/realanalexch.32.1.0087",

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AB - We consider self-similar Borel probability measures μ on a self-similar set E with strong separation property. We prove that for any such measure μ the derivative of its distribution function F(x) is infinite for μ-a.e. x ∈ E, and so the set of points at which F(x) has no derivative, finite or infinite is of μ-zero.

KW - Cantor functions

KW - Non-differentiability

KW - Self-similar measures

KW - Self-similar sets

UR - https://www.scopus.com/pages/publications/72549119849

U2 - 10.14321/realanalexch.32.1.0087

DO - 10.14321/realanalexch.32.1.0087

M3 - 文章

AN - SCOPUS:72549119849

SN - 0147-1937

VL - 32

SP - 87

EP - 96

JO - Real Analysis Exchange

JF - Real Analysis Exchange

IS - 1

ER -

Points of infinite derivative of Cantor functions

Abstract

Keywords

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