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
Statementthe abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Structure theorem for Gaussian measures - Wikipedia
IntroductionQuote, Introduction
the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space
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