Theorem

Structure Theorem for Gaussian Measures

Probability and Statistics

The structure theorem for Gaussian measures, in mathematics, shows that the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space. It was proved during the 1970s, independently, by Kallianpur, Sato, and Stefan, and by Dudley, Feldman, and le Cam.

Facts

Statement

the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space 1

Classification

Statement Form

Characterization Theorem 1

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Has Statement Form

Characterization

In Branch

Measure Theory

Source Structure theorem for Gaussian measures - Wikipedia

Sources

1. Structure theorem for Gaussian measures - Wikipedia

Introduction
the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space
In Branch: Measure Theory, Lead
the structure theorem for Gaussian measures shows that the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space
In Group: Stochastic Processes and Martingales, Lead section
theorem for Gaussian measures shows that the abstract Wiener space construction is essentially the only way

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Structure Theorem for Gaussian Measures

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