Abstract
The Krein–Milman theorem asserts that in a Hausdorff locally convex space all points of a compact convex set can be approximated by convex combinations of its ‘corners’. We show that this can be reinforced to the statement that all points of the set are barycentres of probability measures living on the closure of the extreme points of the set. An interesting application to completely monotone functions on [0, ∞) yields Bernstein’s theorem concerning Laplace transforms of finite Borel measures on [0, ∞).
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Voigt, J. (2020). The Krein–Milman Theorem. In: A Course on Topological Vector Spaces. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-32945-7_17
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DOI: https://doi.org/10.1007/978-3-030-32945-7_17
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