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The Multifractal Spectrum of Quasi Self-Similar Measures

✍ Scribed by Toby C O'Neil

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 305 KB
Volume: 211
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5458

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✦ Synopsis

We define the notion of quasi self-similar measures and show that for such measures their generalised Hausdorff and packing measures are positive and finite at the critical exponent. In practice this allows easy calculation of their dimension functions. We then show that a coarse form of the multifractal formalism automatically holds for quasi self-similar measures. Examples of quasi self-similar measures include many of the standard constructions of multifractal measures satisfying a strong separation condition, in particular, self-similar measures.

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