Dimensions of measure on general Sierpinski carpet

Li Wenxia; Xiao Dongmei

doi:10.1016/s0252-9602(17)30614-8

Dimensions of measure on general Sierpinski carpet

Li Wenxia^*
, Xiao Dongmei

^*Corresponding author for this work

Central China Normal University

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

2 Scopus citations

Abstract

Let S = Π^∞_i=1 {0, 1,⋯, r - 1} and R̄ the general Sierpinski carpet. Let μ be the induced probability measure on R̄ of μ̄ on S by φ, where φ is the natural subjection from S onto R̄ and μ̄ is the infinite product probability measure corresponding to probability vector (b₀,⋯,b_r-1) with b_i = a^{logn m-1}_i/m^α. Authors show that dim_H μ = C_L(μ) = C̄_L(μ) = C(μ) = C̄(μ) = α.

Original language	English
Pages (from-to)	81-85
Number of pages	5
Journal	Acta Mathematica Scientia
Volume	19
Issue number	1
DOIs	https://doi.org/10.1016/s0252-9602(17)30614-8
State	Published - Jan 1999
Externally published	Yes

Keywords

Dimension of measure
General Sierpinski carpet
Probability measure

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title = "Dimensions of measure on general Sierpinski carpet",

abstract = "Let S = Π∞i=1 \{0, 1,⋯, r - 1\} and {\=R} the general Sierpinski carpet. Let μ be the induced probability measure on {\=R} of {\=μ} on S by φ, where φ is the natural subjection from S onto {\=R} and {\=μ} is the infinite product probability measure corresponding to probability vector (b0,⋯,br-1) with bi = alogn m-1i/mα. Authors show that dimH μ = CL(μ) = {\=C}L(μ) = C(μ) = {\=C}(μ) = α.",

keywords = "Dimension of measure, General Sierpinski carpet, Probability measure",

author = "Li Wenxia and Xiao Dongmei",

year = "1999",

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doi = "10.1016/s0252-9602(17)30614-8",

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T1 - Dimensions of measure on general Sierpinski carpet

AU - Wenxia, Li

AU - Dongmei, Xiao

PY - 1999/1

Y1 - 1999/1

N2 - Let S = Π∞i=1 {0, 1,⋯, r - 1} and R̄ the general Sierpinski carpet. Let μ be the induced probability measure on R̄ of μ̄ on S by φ, where φ is the natural subjection from S onto R̄ and μ̄ is the infinite product probability measure corresponding to probability vector (b0,⋯,br-1) with bi = alogn m-1i/mα. Authors show that dimH μ = CL(μ) = C̄L(μ) = C(μ) = C̄(μ) = α.

AB - Let S = Π∞i=1 {0, 1,⋯, r - 1} and R̄ the general Sierpinski carpet. Let μ be the induced probability measure on R̄ of μ̄ on S by φ, where φ is the natural subjection from S onto R̄ and μ̄ is the infinite product probability measure corresponding to probability vector (b0,⋯,br-1) with bi = alogn m-1i/mα. Authors show that dimH μ = CL(μ) = C̄L(μ) = C(μ) = C̄(μ) = α.

KW - Dimension of measure

KW - General Sierpinski carpet

KW - Probability measure

UR - https://www.scopus.com/pages/publications/0041781112

U2 - 10.1016/s0252-9602(17)30614-8

DO - 10.1016/s0252-9602(17)30614-8

M3 - 文章

AN - SCOPUS:0041781112

SN - 0252-9602

VL - 19

SP - 81

EP - 85

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 1

ER -

Dimensions of measure on general Sierpinski carpet

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Keywords

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