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Abstract and Applied Analysis
Volume 2005 (2005), Issue 3, Pages 239-254
http://dx.doi.org/10.1155/AAA.2005.239

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 Hindawi Publishing Corporation. 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.

Abstract

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.