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Intermediate Value Property for the Assouad Dimension of Measures

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Abstract Hare, Mendivil, and Zuberman have recently shown that if X ⊂ ℝ is compact and of non-zero Assouad dimension dimA X, then for all s > dimA X, X… Click to show full abstract

Abstract Hare, Mendivil, and Zuberman have recently shown that if X ⊂ ℝ is compact and of non-zero Assouad dimension dimA X, then for all s > dimA X, X supports measures with Assouad dimension s. We generalize this result to arbitrary complete metric spaces.

Keywords: dimension; property assouad; intermediate value; assouad dimension; value property; dimension measures

Journal Title: Analysis and Geometry in Metric Spaces
Year Published: 2020

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