Linear distortion of Hausdorff dimension and Cantor's function.

Dovgoshey, Oleksiy, et al. "Linear distortion of Hausdorff dimension and Cantor's function.." Collectanea Mathematica 57.2 (2006): 193-210. <http://eudml.org/doc/41836>.

@article{Dovgoshey2006,
abstract = {Let be a mapping from a metric space X to a metric space Y, and let α be a positive real number. Write dim (E) and Hs(E) for the Hausdorff dimension and the s-dimensional Hausdorff measure of a set E. We give sufficient conditions that the equality dim (f(E)) = αdim (E) holds for each E ⊆ X. The problem is studied also for the Cantor ternary function G. It is shown that there is a subset M of the Cantor ternary set such that Hs(M) = 1, with s = log2/log3 and dim(G(E)) = (log3/log2) dim (E), for every E ⊆ M.},
author = {Dovgoshey, Oleksiy, Ryazanov, Vladimir, Martio, Olli, Vuorinen, Matti},
journal = {Collectanea Mathematica},
keywords = {Teoría de la medida; Dimensión de Hausdorff; Conjuntos de Cantor; Cantor function; Cantor ternary set; Hausdorff dimension},
language = {eng},
number = {2},
pages = {193-210},
title = {Linear distortion of Hausdorff dimension and Cantor's function.},
url = {http://eudml.org/doc/41836},
volume = {57},
year = {2006},
}

TY - JOUR
AU - Dovgoshey, Oleksiy
AU - Ryazanov, Vladimir
AU - Martio, Olli
AU - Vuorinen, Matti
TI - Linear distortion of Hausdorff dimension and Cantor's function.
JO - Collectanea Mathematica
PY - 2006
VL - 57
IS - 2
SP - 193
EP - 210
AB - Let be a mapping from a metric space X to a metric space Y, and let α be a positive real number. Write dim (E) and Hs(E) for the Hausdorff dimension and the s-dimensional Hausdorff measure of a set E. We give sufficient conditions that the equality dim (f(E)) = αdim (E) holds for each E ⊆ X. The problem is studied also for the Cantor ternary function G. It is shown that there is a subset M of the Cantor ternary set such that Hs(M) = 1, with s = log2/log3 and dim(G(E)) = (log3/log2) dim (E), for every E ⊆ M.
LA - eng
KW - Teoría de la medida; Dimensión de Hausdorff; Conjuntos de Cantor; Cantor function; Cantor ternary set; Hausdorff dimension
UR - http://eudml.org/doc/41836
ER -