Geodesic
Some generic properties of concentration dimension of measure
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 1, pp. 211-219

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Let $K$ be a compact quasi self-similar set in a complete metric space $X$ and let $\mathfrak{M}_{1}(K)$ 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 $\mathfrak{M}_{1}(K)$ the lower concentration dimension is equal to $0$, while the upper concentration dimension is equal to the Hausdorff dimension of $K$. 
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     author = {Myjak, J\'ozef and Szarek, Tomasz},
     title = {Some generic properties of concentration dimension of measure},
     journal = {Bollettino della Unione matematica italiana},
     pages = {211--219},
     publisher = {mathdoc},
     volume = {Ser. 8, 6B},
     number = {1},
     year = {2003},
     zbl = {1177.28014},
     mrnumber = {MR1955706},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_1_a12/}
}
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Myjak, Józef; Szarek, Tomasz. Some generic properties of concentration dimension of measure. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 1, pp. 211-219. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_1_a12/