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Geometric Aspects of Functional Analysis pp 84–106Cite as

On Milman's inequality and random subspaces which escape through a mesh in ℝ n

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1317))

Abstract

Let S be a subset in the Euclidean space ℝ n and 1 <- k < n. We find sufficient conditions which guarantee the existence and even with probability close to 1, of k-codimensional subspaces which miss S. As a consequence we derive a sharp form of Milman's inequality and discuss some applications to Banach spaces.

Supported in part by the USA-Israel Binational Science Foundation (BSF) grant #86-00074.

Supported in part by the Fund for the Promotion of Research at the Technion #100-700 and the V.P.R. grant #100-677.

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Authors and Affiliations

  1. Technion - Israel Institute of Technology, Haifa, Israel

    Y. Gordon

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  1. Y. Gordon
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Joram Lindenstrauss Vitali D. Milman

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© 1988 Springer-Verlag

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Gordon, Y. (1988). On Milman's inequality and random subspaces which escape through a mesh in ℝ n . In: Lindenstrauss, J., Milman, V.D. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081737

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  • DOI: https://doi.org/10.1007/BFb0081737

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19353-1

  • Online ISBN: 978-3-540-39235-4

  • eBook Packages: Springer Book Archive

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