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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Transfinite multifractal dimension spectrums


Author: Stanley C. Williams
Journal: Trans. Amer. Math. Soc. 348 (1996), 4043-4081
MSC (1991): Primary 28A78, 28A80, 60G42; Secondary 60G57
DOI: https://doi.org/10.1090/S0002-9947-96-01622-4
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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Additional Information

Stanley C. Williams
Affiliation: Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322-3900
Email: williams@sunfs.math.usu.edu

DOI: https://doi.org/10.1090/S0002-9947-96-01622-4
Keywords: Multifractals, dimension spectra, martingales, random measures
Received by editor(s): January 29, 1995
Article copyright: © Copyright 1996 American Mathematical Society