Weak compactness in the space of vector measures

Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces

We give a sequential compactness criterion for the weak topology of vector measures with values in certain nuclear spaces, such as the space S of all rapidly decreasing, infinitely differentiable functions, the space D of all test functions, and the strong duals of those spaces. This result contains Prokhorov–LeCam’s criterion for real measures and applies to cases which are not covered by März...

Weak Compactness in the Space of Operator Valued Measures and Optimal Control

In this paper we present a brief review of some important results on weak compactness in the space of vector valued measures. We also review some recent results of the author on weak compactness of any set of operator valued measures. These results are then applied to optimal structural feedback control for deterministic systems on infinite dimensional spaces.

Weak compactness in the space H1 of martingales

© Springer-Verlag, Berlin Heidelberg New York, 1985, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impressio...

The Strict Topology and Compactness in the Space of Measures

The strict topology j3 on the space C(S) of bounded complex valued continuous functions on a locally compact space 5 was introduced by R. C. Buck [ l ] and has been studied by Glicksberg [4] and Wells [9], Among the problems in mathematics which have seen successful applications of the strict topology are various ones in spectral synthesis (Herz [6]) and spaces of bounded analytic functions (Sh...

Weak Compactness of the Set of ε-Extensions