Multifractal Measures

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The purpose of this dissertation is to introduce a natural and unifying multifractal formalism which contains the above mentioned multifractal parameters, and gives interesting results for a large class of natural measures. In Part 2 we introduce the proposed multifractal formalism and study it properties. We also show that this multifractal formalism gives natural and interesting results when applied to (nonrandom) graph directed self-similar measures in Rd and "cookie-cutter" measures in R. In Part 3 we use the multifractal formalism introduced in Part 2 to give a detailed discussion of the multifractal structure of random (and hence, as a special ... continued below

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vii, 364 leaves: ill.

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Olsen, Lars May 1994.

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  • Olsen, Lars

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Description

The purpose of this dissertation is to introduce a natural and unifying multifractal formalism which contains the above mentioned multifractal parameters, and gives interesting results for a large class of natural measures. In Part 2 we introduce the proposed multifractal formalism and study it properties. We also show that this multifractal formalism gives natural and interesting results when applied to (nonrandom) graph directed self-similar measures in Rd and "cookie-cutter" measures in R. In Part 3 we use the multifractal formalism introduced in Part 2 to give a detailed discussion of the multifractal structure of random (and hence, as a special case, non-random) graph directed self-similar measures in R^d.

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vii, 364 leaves: ill.

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  • May 1994

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  • March 26, 2014, 9:30 a.m.

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  • Nov. 18, 2014, 1:25 p.m.

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Olsen, Lars. Multifractal Measures, dissertation, May 1994; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc279084/: accessed September 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .