Let (f: mathbb{R}^{d} ightarrow mathbb{R}^{n}) be a bi-Lipschitz map, i.e. both (f) and (f^{-1}) are Lipschitz continuous.
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Let \(f: \mathbb{R}^{d} ightarrow \mathbb{R}^{n}\) be a bi-Lipschitz map, i.e. both \(f\) and \(f^{-1}\) are Lipschitz continuous. Show that \(\operatorname{dim} f(E)=\operatorname{dim} E\). Is this also true for a Hölder continuous map with index \(\gamma \in(0,1)\) ?
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Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook
ISBN: 9783110741254
3rd Edition
Authors: René L. Schilling, Björn Böttcher
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