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Theory of Dimension for Large Discrete Sets and Applications
Published online by Cambridge University Press: 17 July 2014
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.
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- Type
- Research Article
- Information
- Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 5: Spectral problems , 2014 , pp. 148 - 169
- Copyright
- © EDP Sciences, 2014
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