Spaces of Probability Measures

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


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.


Probability Measure Characteristic Function Probability Space Open Ball Polish Space 
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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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