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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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: http://dx.doi.org/10.1090/S0002-9939-1991-1045588-X
PII: S 0002-9939(1991)1045588-X
Keywords: Hausdorff dimension, self-affine functions, density topology, density continuity
Article copyright: © Copyright 1991 American Mathematical Society