Distances of Probability Measures and Random Variables

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


Let (S, d) be a separable metric space. Let \( P; > \left( S \right)\) be the set of Borel probability measures on S. \(C\left( S \right)\) denotes the Banach space of bounded continuous real-valued functions on S, with norm
$$\left\| f \right\|_\infty= \sup \left\{ {\left| {f\left( x \right)} \right|:x{\text{ }}\varepsilon {\text{ }}S} \right\}.$$


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • R. M. Dudley
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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