Intermediate Value Property for the Assouad Dimension of Measures

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

• assouad dimension
• intermediate value property
• primary 28a80, 54e50