Theory of Dimension for Large Discrete Sets and Applications
Alex Iosevich, Michael Rudnev, Ignacio Uriarte-Tuero · Mathematical Modelling of Natural Phenomena · 2014
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.