Metric Structures on Families of Metric Spaces

Part of the Modern Birkhäuser Classics book series (MBC)


The Lipschitz distance between two metric spaces X, Y, denoted dL(X, Y), is the infimum of the numbers
$$ |\log dil(f)| + |\log dil(f^{{\text{ - 1}}} )| $$
as f varies over the set of bi-Lipschitz homeomorphisms between X and Y.


Modulus Space Riemannian Manifold Fundamental Group Hausdorff Distance Isometry Group 
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© Birkhäuser Boston 2007

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