The Multifractal Spectrum of Quasi Self-Similar Measures

We define the notion of quasi self-similar measures and show that for such measures their generalised Hausdorff and packing measures are positive and finite at the critical exponent. In practice this allows easy calculation of their dimension functions. We then show that a coarse form of the multifractal formalism automatically holds for quasi self-similar measures. Examples of quasi self-similar measures include many of the standard constructions of multifractal measures satisfying a strong separation condition, in particular, self-similar measures.