# Renewal of singularity sets of statistically self-similar measures

@article{Barral2005RenewalOS, title={Renewal of singularity sets of statistically self-similar measures}, author={Julien Barral and St{\'e}phane Seuret}, journal={arXiv: Probability}, year={2005} }

This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we call the growth speed in Holder singularity sets of a Borel measure. This growth speed yields new…

## 12 Citations

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Let $\{x_n\}_{n\geq 0}$ be a sequence of $[0,1]^d$, $\{\lambda_n\} _{n\geq 0}$ a sequence of positive real numbers converging to 0, and $\delta>1$. Let $\mu$ be a positive Borel measure on $[0,1]^d$,…

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