The Hausdorff dimension of graphs of density continuous functions

Authors:
Zoltán Buczolich and Krzysztof Ostaszewski

Journal:
Proc. Amer. Math. Soc. **112** (1991), 1037-1043

MSC:
Primary 28A78; Secondary 26A15, 54C30

MathSciNet review:
1045588

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Abstract | References | Similar Articles | Additional Information

Abstract: The density topology on the real line consists of all measurable sets whose all points are their points of Lebesgue density one. A real-valued function of a real variable that is continuous with respect to the density topology on both the domain and the range is termed *density continuous*. By constructing graphs of density continuous functions as invariant sets of systems of affine maps on the unit square we show that the Hausdorff dimensions of graphs of density continuous functions vary continuously between one and two.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1045588-X

Keywords:
Hausdorff dimension,
self-affine functions,
density topology,
density continuity

Article copyright:
© Copyright 1991
American Mathematical Society