Multifractal measures definition

In some cases, the limit as r -> 0 is not taken in Equation (2.23) and the ratio r lx By x))/ ar is termed in this case the Holder [36], coarse Holder [37] or Lipschitz-HClder exponent [34]. It is traditionally denoted by a and it may be evaluated for any measure, defined or not by Equation (2.22). This exponent is useful to characterize singular measures, which have no local densities (i.e. for which the limit in Equation (2.23) does not exist), and it plays an important role in the definition of multifractal measures (Section 2.6). 

As with fractals, many authors try to get by without having to provide a precise definition of multifractal measures. Consequently, the term multifractal measure ... 

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