A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Linear distortion of Hausdorff dimension and Cantor's function
Tekijät: Dovgoshey O., Ryazanov V., Martio O., Vuorinen M.
Julkaisuvuosi: 2006
Journal: Collectanea Mathematica
Tietokannassa oleva lehden nimi: Collectanea Mathematica
Vuosikerta: 57
Numero: 2
Aloitussivu: 193
Lopetussivu: 210
Sivujen määrä: 18
ISSN: 0010-0757
Verkko-osoite: http://api.elsevier.com/content/abstract/scopus_id:35348933857
Tiivistelmä
Let f 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 H(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)) = α dim(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 H (M) = 1, with s = log 2/log 3 and dim(G(E)) = (log 3/log2) dim(E), for every E ⊆ M. © 2006 Universitat de Barcelona.
Let f 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 H(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)) = α dim(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 H (M) = 1, with s = log 2/log 3 and dim(G(E)) = (log 3/log2) dim(E), for every E ⊆ M. © 2006 Universitat de Barcelona.
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