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Title: Self-similar sets and measures
Authors: Graf, Siegfried
Issue Date: 1994
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: Siegfried Graf, "Self-similar sets and measures", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 26 (1994) suppl., pp. 35-48.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
26 (1994) suppl.
A major theme in the theory of fractals is that of self—similarity: the whole fractal set is composed of smaller parts which are geometrically similar to whole set. There are several ways to formulate this concept in a mathematically rigorous way. Неге I will deal with Hutchinson’s definition of self-similarity. It is the purpose of this lecture to collect some of the basic results concerning the Hausdorff dimension, Hausdorff measure and local structure of self-similar sets and measures. I am not striving for completeness but rather use my own research interests as a guide to the results and problems in the area. Most of the proofs are omitted. Interested roaders are refered to the literature.
Type: Article
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.26 (1994) s.

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