On a Quasi-Self-Similar Measure on a Self-Similar Set on the Way to a Perturbed Cantor Set

Baek, In-Soo; Baek, In-Soo

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.11 No.1

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On a Quasi-Self-Similar Measure on a Self-Similar Set on the Way to a Perturbed Cantor Set

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2004, v.11 no.1, pp.51-61

Baek, In-Soo

Baek,, I. (2004). On a Quasi-Self-Similar Measure on a Self-Similar Set on the Way to a Perturbed Cantor Set. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 11(1), 51-61.

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Abstract

We find an easier formula to compute Hausdorff and packing dimensions of a subset composing a spectral class by local dimension of a self-similar measure on a self-similar Cantor set than that of Olsen. While we cannot apply this formula to computing the dimensions of a subset composing a spectral class by local dimension of a quasi-self-similar measure on a self-similar set on the way to a perturbed Cantor set, we have a set theoretical relationship between some distribution sets. Finally we compare the behaviour of a quasi-self-similar measure on a self-similar Cantor set with that on a self-similar set on the way to a perturbed Cantor set.

keywords: Hausdorff dimension, packing dimension, Cantor set, distribution set

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Article Contents

Vol.11 No.1

On a Quasi-Self-Similar Measure on a Self-Similar Set on the Way to a Perturbed Cantor Set

Abstract

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics