Lower Bounds for Dimensions of Sums of Sets
Daniel M. Oberlin
TL;DR
This paper investigates the minimum possible Minkowski and Hausdorff dimensions of the sum of two sets in Euclidean space, providing insights into their geometric and dimensional properties.
Contribution
It establishes new lower bounds for the dimensions of sums of sets, advancing understanding of their geometric structure in Euclidean space.
Findings
Derived lower bounds for Minkowski dimensions of set sums
Established lower bounds for Hausdorff dimensions of set sums
Enhanced theoretical understanding of sumset dimensions in Euclidean space
Abstract
We study lower bounds for the Minkowski and Hausdorff dimensions of the algebraic sum E+K of two subsets E and K of d-dimensional Euclidean space.
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Taxonomy
TopicsMathematical Approximation and Integration · Advanced Numerical Analysis Techniques · Digital Image Processing Techniques