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., 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 (6), London: Oxford University Press, pp. xii+393, MR 0426084