The Riesz-Fischer Theorem states that the space of square-integrable functions, and more generally the space of square-summable sequences of coefficients, is complete, meaning every Cauchy sequence of such functions converges to a limit that is again square-integrable. Named for Frigyes Riesz and Ernst Sigismund Fischer, who proved it independently in 1907, it established that the space of square-integrable functions is a genuine Hilbert space, a fact essential to the mathematical foundations of Fourier analysis and quantum mechanics.
Facts
StatementAny of a number of closely related results concerning the properties of the space L2 of square integrable functions. 1 Classification
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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.
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Source Riesz-Fischer theorem (Wikipedia)
Proved By
Source Riesz-Fischer theorem (Wikipedia)
Sources
1. Riesz-Fischer theorem (Wikipedia)
Intro, sentence 1
concerning the properties of the space L2 of square integrable functions
Intro, sentence 2
proven independently in 1907
- In Branch: Real Analysis, Lead sentence
Proved By: Frigyes Riesz, Lead paragraph
In mathematics, the Riesz-Fischer theorem in real analysis is any of a number of closely related results concerning the properties of the space L2
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