On the parametrization of self-similar and other fractal sets

Authors
Martin, MA Mattila, P
Citation
Ma. Martin et P. Mattila, On the parametrization of self-similar and other fractal sets, P AM MATH S, 128(9), 2000, pp. 2641-2648
Citations number
8
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
128
Issue
9
Year of publication
2000
Pages
2641 - 2648
Database
ISI
SICI code
0002-9939(2000)128:9<2641:OTPOSA>2.0.ZU;2-M
Abstract
We prove for many self-similar, and some more general, sets E subset of R-n that if s is the Hausdorff dimension of E and f : R-m --> R-n is Holder co ntinuous with exponent m/s, then the s-dimensional Hausdorff measure of E b oolean AND f(R-m) is 0.