Electronic Resource
Springer
Monatshefte für Mathematik
122 (1996), S. 387-399
ISSN:
1436-5081
Keywords:
28A78
;
28A80
;
Dimension
;
fractal
;
self-similar set
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We analyze self-similarity with respect to infinite sets of similitudes from a measure-theoretic point of view. We extend classic results for finite systems of similitudes satisfying the open set condition to the infinite case. We adopt Vitali-type techniques to approximate overlapping self-similar sets by non-overlapping self-similar sets. As an application we show that any open and bounded set $$A \subseteq \mathbb{R}^n$$ with a boundary of null Lebesgue measure always contains a self-similar set generated by a countable system of similitudes and with Lebesgue measure equal to that ofA.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01326037
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