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Spaces of Probability Measures

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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.

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© 1995 Springer Science+Business Media New York

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Borkar, V.S. (1995). Spaces of Probability Measures. In: Probability Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0791-7_2

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  • DOI: https://doi.org/10.1007/978-1-4612-0791-7_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94558-3

  • Online ISBN: 978-1-4612-0791-7

  • eBook Packages: Springer Book Archive

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