The pointwise densities of non-symmetric cantor sets

Wenxia Li; Yuanyuan Yao

doi:10.1142/S0129167X08005035

The pointwise densities of non-symmetric cantor sets

Wenxia Li^*
, Yuanyuan Yao

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

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

4 Scopus citations

Abstract

We consider a class of non-symmetric Cantor sets C determined by C = a ₀C ∪ (a₁C + 1 - a₁), a₀, a ₁ ∈ (0, 1). Under certain conditions on a₀ and a ₁, the upper and lower densities are obtained explicitly for each x ∈ C. It extends the results for symmetric Cantor sets obtained by Feng, Hua and Wen (The pointwise densities of the Cantor measure, J. Math. Anal. Appl. 250 (2000) 692-705).

Original language	English
Pages (from-to)	1121-1135
Number of pages	15
Journal	International Journal of Mathematics
Volume	19
Issue number	9
DOIs	https://doi.org/10.1142/S0129167X08005035
State	Published - Oct 2008

Keywords

Cantor measure
Non-symmetric Cantor sets
Upper and lower densities.

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abstract = "We consider a class of non-symmetric Cantor sets C determined by C = a 0C ∪ (a1C + 1 - a1), a0, a 1 ∈ (0, 1). Under certain conditions on a0 and a 1, the upper and lower densities are obtained explicitly for each x ∈ C. It extends the results for symmetric Cantor sets obtained by Feng, Hua and Wen (The pointwise densities of the Cantor measure, J. Math. Anal. Appl. 250 (2000) 692-705).",

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N2 - We consider a class of non-symmetric Cantor sets C determined by C = a 0C ∪ (a1C + 1 - a1), a0, a 1 ∈ (0, 1). Under certain conditions on a0 and a 1, the upper and lower densities are obtained explicitly for each x ∈ C. It extends the results for symmetric Cantor sets obtained by Feng, Hua and Wen (The pointwise densities of the Cantor measure, J. Math. Anal. Appl. 250 (2000) 692-705).

AB - We consider a class of non-symmetric Cantor sets C determined by C = a 0C ∪ (a1C + 1 - a1), a0, a 1 ∈ (0, 1). Under certain conditions on a0 and a 1, the upper and lower densities are obtained explicitly for each x ∈ C. It extends the results for symmetric Cantor sets obtained by Feng, Hua and Wen (The pointwise densities of the Cantor measure, J. Math. Anal. Appl. 250 (2000) 692-705).

KW - Cantor measure

KW - Non-symmetric Cantor sets

KW - Upper and lower densities.

UR - https://www.scopus.com/pages/publications/53349172729

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VL - 19

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JO - International Journal of Mathematics

JF - International Journal of Mathematics

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ER -

The pointwise densities of non-symmetric cantor sets

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Keywords

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