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The Hausdorff dimension of the graphs of continuous self-affine functions

Author: M. Urbański
Journal: Proc. Amer. Math. Soc. 108 (1990), 921-930
MSC: Primary 26A30; Secondary 28A75
MathSciNet review: 1000169
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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.

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