Typical multifractal box dimensions of measures
L. Olsen
Fundamenta Mathematicae, Tome 215 (2011), p. 245-266 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We study the typical behaviour (in the sense of Baire’s category) of the multifractal box dimensions of measures on ℝd. 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.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:282864 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-3-3,
     author = {L. Olsen},
     title = {Typical multifractal box dimensions of measures},
     journal = {Fundamenta Mathematicae},
     volume = {215},
     year = {2011},
     pages = {245-266},
     zbl = {1215.28008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-3-3}
}

L. Olsen. Typical multifractal box dimensions of measures. Fundamenta Mathematicae, Tome 215 (2011) pp. 245-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-3-3/