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In mathematics, Sazonov's theorem, named after Vyacheslav Vasilievich Sazonov (), is a theorem in functional analysis. It states that a bounded linear operator between two Hilbert spaces is ''γ''-radonifying if it is Hilbert–Schmidt. 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. ==Statement of the theorem== Let ''G'' and ''H'' be two Hilbert spaces and let ''T'' : ''G'' → ''H'' be a bounded operator from ''G'' to ''H''. Recall that ''T'' is said to be ''γ''-radonifying if the push forward of the canonical Gaussian cylinder set measure on ''G'' is a ''bona fide'' measure on ''H''. Recall also that ''T'' is said to be Hilbert–Schmidt if there is an orthonormal basis of ''G'' such that : Then Sazonov's theorem is that ''T'' is ''γ''-radonifying if it is Hilbert–Schmidt. The proof uses Prokhorov's theorem. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sazonov's theorem」の詳細全文を読む スポンサード リンク
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