Abstract
There are many results in probability theory on vector spaces which rely implicitly on the approximation of a given cylindrical probability by cylindrical probabilities with moments; for example, this is the basic idea behind the proof of the Radon equivalence of the weak and strong topologies of a metrizable space (Schwartz [13] p. 162). The technique of approximation by cylindrical measures with moments can be systematically developed. In particular, it follows that if each member of a family of cylindrical probabilities with moments is decomposable, then the limits of these cylindrical probabilities are often regular and so they are σ-additive.
Publisher
Cambridge University Press (CUP)
Reference15 articles.
1. Quantum Physics
2. The Lebesgue-Nikodym Theorem for Vector Valued Radon Measures
3. Topological Vector Spaces
4. Mesures cylindriques sur les espaces de Banach qui ont le Radon-Nikodým;Schachermayer;C.R. Acad. Sci. Paris, Ser.,1976