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Hilbertian support of a probability measure on a banach space

Part of the Lecture Notes in Mathematics book series (LNM,volume 709)

Abstract

In this paper, we will prove the following : Let E be a real separable Banach space. Then every probability measure on E has a Hilbertian support if and only if E is isomorphic to a Hilbert space. In the case of l p (1 ≤ p < 2) we will give an explicit construction of probability measures without Hilbertian support.

Keywords

  • Hilbert Space
  • Banach Space
  • Probability Measure
  • Bilinear Form
  • Gaussian Measure

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© 1979 Springer-Verlag

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Sato, H. (1979). Hilbertian support of a probability measure on a banach space. In: Beck, A. (eds) Probability in Banach Spaces II. Lecture Notes in Mathematics, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071958

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  • DOI: https://doi.org/10.1007/BFb0071958

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09242-1

  • Online ISBN: 978-3-540-35341-6

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