Minlos's theorem

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 hide vte Functional analysis (topics – glossary) Spaces BanachBesovFréchetHilbertHölderNuclearOrliczSchwartzSobolevtopological vector Properties barrelledcompletedual (algebraic/topological)locally convexreflexiveseparable Theorems Hahn–BanachRiesz representationclosed graphuniform boundedness principleKakutani fixed-pointKrein–Milmanmin–maxGelfand–NaimarkBanach–Alaoglu Operators adjointboundedcompactHilbert–Schmidtnormalnucleartrace classtransposeunboundedunitary Algebras Banach algebraC*-algebraspectrum of a C*-algebraoperator algebragroup algebra of a locally compact groupvon Neumann algebra Open problems invariant subspace problemMahler's conjecture Applications Hardy spacespectral theory of ordinary differential equationsheat kernelindex theoremcalculus of variationsfunctional calculusintegral operatorJones polynomialtopological quantum field theorynoncommutative geometryRiemann hypothesisdistribution (or generalized functions) Advanced topics approximation propertybalanced setChoquet theoryweak topologyBanach–Mazur distanceTomita–Takesaki theory This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.

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