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Spaces of Probability Measures

  • Vivek S. Borkar
Part of the Universitext book series (UTX)

Abstract

Let S be a Polish space with a complete metric d taking values in [0,1] and P(S) the space of probability measures on S. Recall the map h : S → [0,1] of Theorem 1.1.1. Since \( \overline {h(S)} \) is compact, \( \overline {C(h(s)} ) \) is separable. Let fi be countable dense in the unit ball of \( \overline {C(h(s)} ) \) and {f′ i} their restrictions to h(h). Define {fi} ⊂ Cb(S) (= the space of bounded continuous functions S → R) by fi = fi o h, i ≥ 1.

Keywords

Probability Measure Characteristic Function Probability Space Open Ball Polish Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Vivek S. Borkar
    • 1
  1. 1.Department of Electrical EngineeringIndian Institute of ScienceBangaloreIndia

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