Inversion Formula for Continuous Multifractals
نویسندگان
چکیده
In a previous paper MR the authors introduced the inverse measure y of a probability measure on It was argued that the respective multifractal spectra are linked by the inversion formula fy f 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 Hausdor spectrum the packing spectrum or the coarse grained spectrum With a closer look at the special case of self similar measures we o er a motivation of the inversion formula as well as a discussion of possible generalizations Doing so we nd a natural extension of the scope of the notion self similar and a failure of the usual multifractal formalism Facsimile for personal use c Academic Press
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