Riedi, Rudolf H.Mandelbrot, Benoit2007-10-312007-10-311997-01-202004-01-14R. H. Riedi and B. Mandelbrot, "Inversion Formula for Continuous Multifractals," <i>Advances in Applied Mathematics,</i> 1997.https://hdl.handle.net/1911/20267Journal PaperIn a previous paper the authors introduced the inverse measure <i>µ</i>^â of a probability measure <i>µ</i> on [0,1]. It was argued that the respective multifractal spectra are linked by the 'inversion formula' <i>f</i>^â(<i>a</i>) = <i>a</i><i>f</i>(1/<i>a</i>). Here, the statements of Part I are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures. Thereby, <i>f</i> may stand for the Hausdorff spectrum, the pacing spectrum, or the coarse grained spectrum. With a closer look at the special case of self-similar measures we offer a motivation of the inversion formula as well as a discussion of possible generalizations. Doing so we find a natural extension of the scope of the notion 'self-similar' and a failure of the usual multifractal formalism.engTemporaryMultifractalsJournal articleTemporaryhttp://dx.doi.org/10.1006/aama.1997.0550