About: Sazonov's theorem

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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.

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rdfs:label	Sazonov's theorem (en) Теорема Сазонова (ru)
rdfs:comment	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. (en) Теорема Сазонова относится к области функционального анализа. Теорема утверждает, что ограниченный линейный оператор между двумя Гильбертовыми пространствами является , если это оператор Гильберта — Шмидта.Так же верно и обратное: если оператор не Гильберта-Шмидта, то он не является . Результат также важен при изучении случайных процессов и , так как результаты, касающиеся вероятностной меры на бесконечномерных пространствах имеют центральное значение в этих областях. (ru)
dct:subject	Theorems in functional analysis Stochastic processes
Wikipage page ID	9196302 (xsd:integer)
Wikipage revision ID	987115765 (xsd:integer)
Link from a Wikipage to another Wikipage	Cylinder set measure Theorems in functional analysis Mathematics Measure (mathematics) Bounded operator Theorem Pushforward measure Stochastic processes Functional analysis Orthonormal basis Hilbert–Schmidt operator Prokhorov's theorem Hilbert space Stochastic processes Identity function Malliavin calculus Probability measure Vyacheslav Vasilievich Sazonov Γ-radonifying
sameAs	Sazonov's theorem Sazonov's theorem Sazonov's theorem Sazonov's theorem Sazonov's theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Functional_analysis
has abstract	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. (en) Теорема Сазонова относится к области функционального анализа. Теорема утверждает, что ограниченный линейный оператор между двумя Гильбертовыми пространствами является , если это оператор Гильберта — Шмидта.Так же верно и обратное: если оператор не Гильберта-Шмидта, то он не является . Результат также важен при изучении случайных процессов и , так как результаты, касающиеся вероятностной меры на бесконечномерных пространствах имеют центральное значение в этих областях. (ru)
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is Link from a Wikipage to another Wikipage of	Cylinder set measure Minlos's theorem Catalog of articles in probability theory Sazonov List of statistics articles List of theorems Vyacheslav Vasilievich Sazonov Sazonov theorem
is Wikipage redirect of	Sazonov theorem
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