Some generic properties of concentration dimension of measure

Myjak, Józef; Szarek, Tomasz

Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003), p. 211-219 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

Let $K$ be a compact quasi self-similar set in a complete metric space $X$ and let $M_{1} (K)$ denote the space of all probability measures on $K$ , endowed with the Fortet-Mourier metric. We will show that for a typical (in the sense of Baire category) measure in $M_{1} (K)$ the lower concentration dimension is equal to $0$ , while the upper concentration dimension is equal to the Hausdorff dimension of $K$ .

Sia $K$ un sottoinsieme quasi similare compatto di uno spazio metrico completo. Sia $M_{1} (K)$ lo spazio delle misure di probabilità su $K$ munito della metrica di Fortet-Mourier. Si dimostra che per una misura $μ \in M_{1} (K)$ tipica (nel senzo della categoria di Baire) la dimensione inferiore di concentrazione è uguale a zero, invece la dimensione superiore di concentrazione è uguale alla dimensione di Hausdorff dell'insieme $K$ .

Publié le : 2003-02-01

MR 1955706 | Zbl 1177.28014

@article{BUMI_2003_8_6B_1_211_0,
     author = {J\'ozef Myjak and Tomasz Szarek},
     title = {Some generic properties of concentration dimension of measure},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {6-A},
     year = {2003},
     pages = {211-219},
     zbl = {1177.28014},
     mrnumber = {1955706},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2003_8_6B_1_211_0}
}

Myjak, Józef; Szarek, Tomasz. Some generic properties of concentration dimension of measure. Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003) pp. 211-219. http://gdmltest.u-ga.fr/item/BUMI_2003_8_6B_1_211_0/

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