Abstract
Let \(E\) be a subset of a doubling metric space \((X,d)\). We prove that for any \(s\in [0, \dim_{A}E]\), where \(\dim_{A}\) denotes the Assouad dimension, there exists a subset \(F\) of \(E\) such that \(\dim_{A}F=s\). We also show that the same statement holds for the lower dimension \(\dim_L\).
Citation
Changhao Chen. Meng Wu. Wen Wu. "Accessible Values for the Assouad and Lower Dimensions of Subsets." Real Anal. Exchange 45 (1) 85 - 100, 2020. https://doi.org/10.14321/realanalexch.45.1.0085
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