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ISSN 1088-6850(e) ISSN 0002-9947(p)

Transfinite multifractal dimension spectrums

Author(s): Stanley C. Williams
Journal: Trans. Amer. Math. Soc. 348 (1996), 4043-4081.
MSC (1991): Primary 28A78, 28A80, 60G42; Secondary 60G57
MathSciNet review: 1351496
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Abstract: The first order theory of the decomposition of measures with respect to dimension which has been developed by Kahane, Katznelson, Cutler, and others is extended through transfinite recursion to a $\omega _1$ -order theory. Necessary and sufficient conditions for a finite regular Borel measure on $% [0,d]^{\omega _1}$ to be a $\omega _1$ -order multispectrum for a finite Borel measure on $\mathbb {R}^d$ is given.

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