Existence of L-q dimensions and entropy dimension for self-conformal measures

Authors
Peres, Y Solomyak, B
Citation
Y. Peres et B. Solomyak, Existence of L-q dimensions and entropy dimension for self-conformal measures, INDI MATH J, 49(4), 2000, pp. 1603-1621
Citations number
27
Categorie Soggetti
Mathematics
Journal title
INDIANA UNIVERSITY MATHEMATICS JOURNAL
ISSN journal
00222518 → ACNP
Volume
49
Issue
4
Year of publication
2000
Pages
1603 - 1621
Database
ISI
SICI code
0022-2518(200024)49:4<1603:EOLDAE>2.0.ZU;2-3
Abstract
We prove the existence of limits in the definitions of L-q dimensions, q > 0, q not equal 1, and the entropy dimension for any self-conformal measure, without any separation assumptions. We also show the existence of order-tw o densities for a class of self-similar measures with overlap.