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 = f′i 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
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