Lipschitz representations of subsets of the cube

Shahar Mendelson*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    We show that for any class of uniformly bounded functions H with a reasonable combinatorial dimension, the vast majority of small subsets of the n-dimensional combinatorial cube cannot be represented as a Lipschitz image of a subset of H, unless the Lipschitz constant is very large. We apply this result to the case when H consists of linear functionals of norm at most one on a Hilbert space.

    Original languageEnglish
    Pages (from-to)1455-1463
    Number of pages9
    JournalProceedings of the American Mathematical Society
    Issue number5
    Publication statusPublished - May 2007


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