Typical multifractal box dimensions of measures

L. Olsen. "Typical multifractal box dimensions of measures." Fundamenta Mathematicae 211.3 (2011): 245-266. <http://eudml.org/doc/282864>.

@article{L2011,
abstract = {We study the typical behaviour (in the sense of Baire’s category) of the multifractal box dimensions of measures on $ℝ^\{d\}$. We prove that in many cases a typical measure μ is as irregular as possible, i.e. the lower multifractal box dimensions of μ attain the smallest possible value and the upper multifractal box dimensions of μ attain the largest possible value.},
author = {L. Olsen},
journal = {Fundamenta Mathematicae},
keywords = {multifractals; -dimensions; Rényi dimensions; Baire category; co-meagre set},
language = {eng},
number = {3},
pages = {245-266},
title = {Typical multifractal box dimensions of measures},
url = {http://eudml.org/doc/282864},
volume = {211},
year = {2011},
}

TY - JOUR
AU - L. Olsen
TI - Typical multifractal box dimensions of measures
JO - Fundamenta Mathematicae
PY - 2011
VL - 211
IS - 3
SP - 245
EP - 266
AB - We study the typical behaviour (in the sense of Baire’s category) of the multifractal box dimensions of measures on $ℝ^{d}$. We prove that in many cases a typical measure μ is as irregular as possible, i.e. the lower multifractal box dimensions of μ attain the smallest possible value and the upper multifractal box dimensions of μ attain the largest possible value.
LA - eng
KW - multifractals; -dimensions; Rényi dimensions; Baire category; co-meagre set
UR - http://eudml.org/doc/282864
ER -