On the parametrization of self-similar and other fractal sets
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- by Miguel Angel Martín and Pertti Mattila PDF
- Proc. Amer. Math. Soc. 128 (2000), 2641-2648 Request permission
Abstract:
We prove for many self-similar, and some more general, sets $E \subset \mathbb {R}^{n}$ that if $s$ is the Hausdorff dimension of $E$ and $f: \mathbb {R}^{m} \to \mathbb {R}^{n}$ is Hölder continuous with exponent $m/s$, then the $s$-dimensional Hausdorff measure of $E \cap f(\mathbb {R}^{m})$ is $0$.References
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Additional Information
- Miguel Angel Martín
- Affiliation: Departamento de Matemática Aplicada, E.T.S.I. Agrónomos, Universidad Politécnica de Madrid, 28040 Madrid, Spain
- MR Author ID: 643000
- ORCID: 0000-0003-4502-798X
- Email: mamartin@mat.etsia.upm.es
- Pertti Mattila
- Affiliation: Department of Mathematics, University of Jyväskylä, P. O. Box 35, FIN-40351 Jyväskylä, Finland
- MR Author ID: 121505
- Email: pmattila@math.jyu.fi
- Received by editor(s): June 4, 1998
- Received by editor(s) in revised form: October 20, 1998
- Published electronically: March 1, 2000
- Additional Notes: This work was partially done while P. Mattila was visiting the Centre de Recerca Matemàtica in Barcelona supported by the Ministerio de Educacion y Cultura.
- Communicated by: Albert Baernstein II
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2641-2648
- MSC (2000): Primary 28A75, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-00-05354-5
- MathSciNet review: 1664402