Mixed generalized dimensions of self-similar measures

Classical multifractal analysis studies the local scaling behaviour of a single measure. However, recently mixed multifractal has generated interest. Mixed multifractal analysis studies the simultaneous scaling behaviour of finitely many measures and provides the basis for a significantly better understanding of the local geometry of fractal measures. The purpose of this paper is twofold. Firstly, we define and develop a general and unifying mixed multifractal theory of mixed Renyi dimensions (also sometimes called the generalized dimensions), mixed L-q-dimensions and mixed coarse multifractal spectra for arbitrary doubling measures. Secondly, as an application of the general theory developed in this paper, we provide a complete description of the mixed multifractal theory of finitely many self-similar measures. (c) 2004 Elsevier Inc. All rights reserved.