In good cases, we prove that the function $\tau$ which appears in multifractal formalism is adapted to calculate the lower and the upper dimension of a measure. Then, we are able to prove the derivability of $\tau$ for quasi-Bernoulli measures, thus precising some of Brown Michon and Peyrière results concerning the multifractal analysis of these measures.
Publié le : 1998-07-05
Classification:
Mesure de Hausdorff,
Mesure de packing,
Dimension de Hausdorff,
Dimension de Tricot,
Dimension inférieure et supérieure,
Analyse multifractale,
28A12 - 28A78 - 28D05 - 28D20 - 60F10,
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
@article{hal-00475644,
author = {Heurteaux, Yanick},
title = {Estimations de la dimension inf\'erieure et de la dimension sup\'erieure des mesures},
journal = {HAL},
volume = {1998},
number = {0},
year = {1998},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00475644}
}
Heurteaux, Yanick. Estimations de la dimension inférieure et de la dimension supérieure des mesures. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-00475644/