High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, Sazonov's theorem is a theorem in functional analysis. It states that a bounded linear operator between two Hilbert spaces is ?-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 ?-radonifying.

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