Self-similar sets in complete metric spaces

Author:
Andreas Schief

Journal:
Proc. Amer. Math. Soc. **124** (1996), 481-490

MSC (1991):
Primary 28A80, 28A78

DOI:
https://doi.org/10.1090/S0002-9939-96-03158-9

MathSciNet review:
1301047

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Abstract: We develop a theory for Hausdorff dimension and measure of self-similar sets in complete metric spaces. This theory differs significantly from the well-known one for Euclidean spaces. The open set condition no longer implies equality of Hausdorff and similarity dimension of self-similar sets and that has nonzero Hausdorff measure in this dimension. We investigate the relationship between such properties in the general case.

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Additional Information

**Andreas Schief**

Affiliation:
Corporate Research and Development, SIEMENS AG, 81730, Munich, Germany

Email:
andreas.schief@zfe.siemens.de

DOI:
https://doi.org/10.1090/S0002-9939-96-03158-9

Keywords:
SOSC,
OSC,
self-similar sets,
fractals,
Hausdorff dimension,
complete metric spaces

Received by editor(s):
June 9, 1994

Received by editor(s) in revised form:
August 23, 1994

Communicated by:
Christopher D. Sogge

Article copyright:
© Copyright 1996
American Mathematical Society