Riesz-Fischer Theorem
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Contents
Theorem
Let $\left({X, \Sigma, \mu}\right)$ be a measure space.
Let $p \in \R$, $p \ge 1$.
The Lebesgue $p$-space $\mathcal L^p \left({\mu}\right)$, endowed with the $p$-norm, is a complete metric space.
Proof
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Source of Name
This entry was named for Frigyes Riesz and Ernst Sigismund Fischer.
Fischer proved the result for $p = 2$, while Riesz (independently) proved it for all $p \ge 1$.
Sources
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $12.7$
