VALIDITY of the multifractal formalism under the box condition

In this paper, we intend to generalise the work of Banal et al. (2003) [1 I, which provides a bridge between the c-adic boxes and the grid-free approaches to the multifractal analysis of measures. More precisely, we consider some sort of an irregular grid. We apply our results to a Bernoulli measure. (C) 2015 Published by Elsevier Ltd.