Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Self-similar sets in complete metric spaces
HTML articles powered by AMS MathViewer

by Andreas Schief PDF
Proc. Amer. Math. Soc. 124 (1996), 481-490 Request permission

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 $K$ has nonzero Hausdorff measure in this dimension. We investigate the relationship between such properties in the general case.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28A80, 28A78
  • Retrieve articles in all journals with MSC (1991): 28A80, 28A78
Additional Information
  • Andreas Schief
  • Affiliation: Corporate Research and Development, SIEMENS AG, 81730, Munich, Germany
  • Email: andreas.schief@zfe.siemens.de
  • Received by editor(s): June 9, 1994
  • Received by editor(s) in revised form: August 23, 1994
  • Communicated by: Christopher D. Sogge
  • © Copyright 1996 American Mathematical Society
  • 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