Minlos's theorem

In the mathematics of topological vector spaces, Minlos's theorem states that a cylindrical measure on the dual of a nuclear space is a Radon measure if its Fourier transform is continuous. It is named after Robert Adol'fovich Minlos and can be proved using Sazonov's theorem.

References

Minlos, R. A. (1963), Generalized random processes and their extension to a measure, Selected Transl. Math. Statist. and Prob., vol. 3, Providence, R.I.: Amer. Math. Soc., pp. 291–313, MR 0154317
Schwartz, Laurent (1973), Radon measures on arbitrary topological spaces and cylindrical measures, Tata Institute of Fundamental Research Studies in Mathematics, London: Oxford University Press, pp. xii+393, MR 0426084

Functional analysis (topics – glossary)

Spaces

Banach Besov Fréchet Hilbert Hölder Nuclear Orlicz Schwartz Sobolev Topological vector
Properties	Barrelled Complete Dual (Algebraic/Topological) Locally convex Reflexive Separable