A simple example of a nonclosed set of representing measures

• Autorzy: Puchała, P.
• Języki publikacji: EN

Abstrakty

EN

Let X be a locally convex Hausdorff space, K - its compact, convex and metrizable subset. We say, that a regular Borel probability measure μ on K represents point x;ϵX if the equality f(x) = ∫fdμ holds for every f ϵ X*. We will show by a simple example, that the set of such measures supported on ext K need not be closed.

Słowa kluczowe

EN

representing measures

• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2002
• Tom: Vol. 1, nr 1
• Strony: 197--199
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Puchała, P.

• Institute of Mathematics and Computer Science, Technical University of Częstochowa

Bibliografia

• [1] Choquet G., Lectures on analysis, vols. I, II, III, Lecture Notes in Mathematics, W.A. Bejamin 1969.
• [2] Phelps R.R., Lectures on Choquet’s theorem, 2nd ed., Lecture Notes in Mathematics, Springer 2001.
• [3] Parthasarathy K.R., Probability measures on metric spaces, Academic Press 1967.