Theorems in functional analysis | Stochastic processes

Sazonov's theorem

In mathematics, Sazonov's theorem, named after Vyacheslav Vasilievich Sazonov (Вячесла́в Васи́льевич Сазо́нов), is a theorem in functional analysis. It states that a bounded linear operator between two Hilbert spaces is γ-radonifying if it is a Hilbert–Schmidt operator. The result is also important in the study of stochastic processes and the Malliavin calculus, since results concerning probability measures on infinite-dimensional spaces are of central importance in these fields. Sazonov's theorem also has a converse: if the map is not Hilbert–Schmidt, then it is not γ-radonifying. (Wikipedia).

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Related pages

Prokhorov's theorem | Hilbert space | Bounded operator | Identity function | Functional analysis | Mathematics | Probability measure | Measure (mathematics) | Orthonormal basis | Theorem | Hilbert–Schmidt operator | Pushforward measure | Cylinder set measure | Malliavin calculus