Minlos' theorem

In mathematics, Minlos' theorem states that a cylindrical measure on the dual of a nuclear space is a Radon measure if its Fourier transform is continuous. It can be proved using Sazonov's theorem.

[edit] References

Minlos, R. A. (1963), Generalized random processes and their extension to a measure, vol. 3, Selected Transl. Math. Statist. and Prob., 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