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Abstract: In a previous paper [MR] the authors introduced the inverse measure of a probability measure on [0; 1]. It was argued that the respective multifractal spectra are linked by the `inversion formula' f (ff) = fff(1=ff). Here, the statements of [MR] are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures. Thereby, f may stand for the Hausdorff spectrum, the packing spectrum, or the coarse grained spectrum. With a closer look ... (Update)
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BibTeX entry: (Update)
R. H. Riedi and B. B Mandelbrot, The Inversion Formula for Continuous Multifractals, Adv. Appl. Math. 19 (1997) pp 332--354 http://citeseer.ist.psu.edu/riedi97inversion.html More
@misc{ riedi97inversion,
author = "R. Riedi and B. Mandelbrot",
title = "The Inversion Formula for Continuous Multifractals",
text = "R. H. Riedi and B. B Mandelbrot, The Inversion Formula for Continuous Multifractals,
Adv. Appl. Math. 19 (1997) pp 332--354",
year = "1997",
url = "citeseer.ist.psu.edu/riedi97inversion.html" }
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