The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes

  • R. M. Dudley
Part of the Selected Works in Probability and Statistics book series (SWPS)


The first two sections of this paper are introductory and correspond to the two halves of the title. As is well known, there is no complete analog of Lebesue or Haar measure in an infinite-dimensional Hilbert space H, but there is a need for some measure of the sizes of subsets of H. In this paper we shall study subsets C of H which are closed, bounded, convex and symmetric (— x ε C if x ε C). Such a set C will be called a Banach ball, since it is the unit ball of a complete Banach norm on its linear span. In most cases in this paper C will be compact.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • R. M. Dudley
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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