Abstract
As was seen in Proposition 1.1, the resultant map from the probability measures P(X) onto the compact convex set X is affine and weak* continuous. By the Choquet-Bishop-deLeeuw theorem, its restriction r to the set Q(X) of maximal probability measures is still surjective, and from the uniqueness theorem we know that r is bijective if and only if X is a simplex. In this section we prove some additional properties of this map, including a simple but potentially useful selection theorem for the metrizable case.
Keywords
- Compact Hausdorff Space
- Dense Subspace
- Metrizable Case
- Selection Theorem
- Baire Class
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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). Properties of the resultant map. In: Phelps, R.R. (eds) Lectures on Choquet’s Theorem. Lecture Notes in Mathematics, vol 1757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48719-0_11
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DOI: https://doi.org/10.1007/3-540-48719-0_11
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41834-4
Online ISBN: 978-3-540-48719-7
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