The multifractal spectrum of statistically self-similar measures (Q1332410)

The author defines the concepts of a statistically self-similar measure on a random subset \(F\) of \(R^ n\), and of multifractal components of \(F\). It is proved that with probability one there is a multifractal decomposition analogous to that in the deterministic self-similar case. In a note added in proof, the author points out that, in the book ``Random geometrically graph directed self-similar multifractals'' (1994; Zbl 0801.28002)], \textit{L. Olsen} extends the results obtained in the present paper and addresses many aspects of the problems discussed in very full detail.