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Ultrametric skeletons

We prove that for every ε∈(0,1) there exists C(ε)∈(0,∞) with the following property. If (X,d) is a compact metric space and μ is a Borel probability measure on X then there exists a compact subset S⊆X that embeds into an ultrametric space with distortion O(1/ε), and a probability measure ν supported...

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Bibliographic Details
Main Authors: Mendel, Manor, Naor, Assaf
Format: Artigo
Language:Inglês
Published: National Academy of Sciences 2013
Subjects:
Online Access:https://ncbi.nlm.nih.gov/pmc/articles/PMC3845111/
https://ncbi.nlm.nih.govhttp://dx.doi.org/10.1073/pnas.1202500109
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