Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on Hausdorff measures of quasi-self-similar sets


Author: John McLaughlin
Journal: Proc. Amer. Math. Soc. 100 (1987), 183-186
MSC: Primary 54H20; Secondary 28A75, 58F12
MathSciNet review: 883425
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Sullivan has demonstrated that quasi-self-similarity provides a useful point of view for the study of expanding dynamical systems. In [4, p. 57] he posed the question: Is the Hausdorff measure of a quasi-self-similar set positive and finite in its Hausdorff dimension? This paper answers both parts of this question. In $ \S1$ the positivity is established for compact sets, and a lower bound is given for their Hausdorff measure. However, in $ \S2$ the finiteness is disproved. In fact, a quasi-self-similar set is constructed for which the Hausdorff measure is actually $ \sigma $-infinite.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H20, 28A75, 58F12

Retrieve articles in all journals with MSC: 54H20, 28A75, 58F12


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0883425-3
PII: S 0002-9939(1987)0883425-3
Keywords: Self-similarity Hausdorff measure
Article copyright: © Copyright 1987 American Mathematical Society