Journal of Mathematics of Kyoto University

Spectra of deranged Cantor set by weak local dimensions

In-Soo Baek

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Abstract

We decompose the most generalized Cantor set into a spectral class using weak lower (upper) local dimension. Each member of the spectral class is related to a quasi-self-similar measure, so the information of its Hausdorff (packing) dimension can be obtained. In the end, we give an example of the Cantor set having countable members composing the spectral class.

Article information

Source
J. Math. Kyoto Univ., Volume 44, Number 3 (2004), 493-500.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283080

Digital Object Identifier
doi:10.1215/kjm/1250283080

Mathematical Reviews number (MathSciNet)
MR2103779

Zentralblatt MATH identifier
1109.28004

Subjects
Primary: 28A78: Hausdorff and packing measures
Secondary: 28A80: Fractals [See also 37Fxx]

Citation

Baek, In-Soo. Spectra of deranged Cantor set by weak local dimensions. J. Math. Kyoto Univ. 44 (2004), no. 3, 493--500. doi:10.1215/kjm/1250283080. https://projecteuclid.org/euclid.kjm/1250283080


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