The Hausdorff dimension of the graphs of continuous self-affine functions
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- by M. Urbański
- Proc. Amer. Math. Soc. 108 (1990), 921-930
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000169-8
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Abstract:
The exact formula for the Hausdorff dimension of the graph of a continuous self-affine function is obtained. The Hausdorff dimension of some class of Borel probability measures is computed. The Hausdorff measures corresponding to the functions ${\varphi _c}(t) = {t^{HD({\text {graph}}(f))}}\exp (c\sqrt {\log 1/t\log \log \log 1/t}$ are studied.References
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Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 921-930
- MSC: Primary 26A30; Secondary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000169-8
- MathSciNet review: 1000169