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arXiv · 0707.1322

Theory of dimension for large discrete sets and applications

Alex Iosevich·Misha Rudnev·Ignacio Uriarte-Tuero
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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 Erdos and Falconer distance problems in geometric combinatorics and geometric measure theory, respectively.

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Alex Iosevich, Misha Rudnev, Ignacio Uriarte-Tuero. 2007-07-09. Theory of dimension for large discrete sets and applications. https://arxiv.org/abs/0707.1322

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