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Theory of Dimension for Large Discrete Sets and Applications

Published online by Cambridge University Press:  17 July 2014

A. Iosevich
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY 14627
M. Rudnev
Affiliation:
Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK
I. Uriarte-Tuero
Affiliation:
Department of Mathematics, Michigan State University, East Lansing MI 48824
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Abstract

We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections between the Erdős and Falconer distance problems in geometric combinatorics and geometric measure theory, respectively.

Type
Research Article
Copyright
© EDP Sciences, 2014

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References

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