Abstract and Applied Analysis
Volume 2005 (2005), Issue 3, Pages 239-254
Some typical properties of dimensions of sets and measures
1Dipartimento di Matematica Pura ed Applicata, Università dell'Aquila, via Vetoio, l'Aquila 67010, Italy
2Wydzial Matematyki Stosowanej, Akademia Górniczo-Hutnicza, Al. Mickiewicza 30, Kraków 30059, Poland
Received 2 January 2004
Copyright © 2005 Józef Myjak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper contains a review of recent results concerning typical
properties of dimensions of sets and dimensions of measures. In
particular, we are interested in the Hausdorff dimension, box
dimension, and packing dimension of sets and in the Hausdorff
dimension, box dimension, correlation dimension, concentration
dimension, and local dimension of measures.