Some generic properties of concentration dimension of measure
Bollettino dell'Unione Matematica Italiana (2003)
- Volume: 6-B, Issue: 1, page 211-219
- ISSN: 0392-4041
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topMyjak, Józef, and Szarek, Tomasz. "Some generic properties of concentration dimension of measure." Bollettino dell'Unione Matematica Italiana 6-B.1 (2003): 211-219. <http://eudml.org/doc/195320>.
@article{Myjak2003,
abstract = {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 $K$.},
author = {Myjak, Józef, Szarek, Tomasz},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {211-219},
publisher = {Unione Matematica Italiana},
title = {Some generic properties of concentration dimension of measure},
url = {http://eudml.org/doc/195320},
volume = {6-B},
year = {2003},
}
TY - JOUR
AU - Myjak, Józef
AU - Szarek, Tomasz
TI - Some generic properties of concentration dimension of measure
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/2//
PB - Unione Matematica Italiana
VL - 6-B
IS - 1
SP - 211
EP - 219
AB - 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 $K$.
LA - eng
UR - http://eudml.org/doc/195320
ER -
References
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