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math.CA2019
Measures with specified support and arbitrary Assouad dimensions
Kathryn E. Hare, Franklin Mendivil, Leandro Zuberman
We show that if the upper Assouad dimension of the compact set is positive, then given any there is a measure with support and upper Assou…
math.CA2019
Almost sure Assouad-like Dimensions of Complementary sets
Ignacio García, Kathryn E. Hare, Franklin Mendivil
Given a non-negative, decreasing sequence with sum , we consider all the closed subsets of such that the lengths of their complementary open intervals are given by t…
math.CA2019
Intermediate Assouad-like dimensions
Ignacio García, Kathryn Hare, Franklin Mendivil
We introduce and study bi-Lipschitz-invariant dimensions that range between the box and Assouad dimensions. The quasi-Assouad dimensions and -spectrum are other special examples…