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Egorov's theorem (Theorem)

Let $ (X,\mathcal{S},\mu)$ be a measure space, and let $ E$ be a subset of $ X$ of finite measure. If $ f_n$ is a sequence of measurable functions converging to $ f$ almost everywhere, then for each $ \delta>0$ there exists a set $ E_\delta$ such that $ \mu(E_\delta)<\delta$ and $ f_n\rightarrow f$ uniformly on $ E-E_\delta$.



"Egorov's theorem" is owned by Koro.
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Other names:  Egoroff's theorem

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proof of Egorov's theorem (Proof) by Koro
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Cross-references: almost everywhere, measurable functions, sequence, measure, finite, subset, measure space
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This is version 3 of Egorov's theorem, born on 2002-12-09, modified 2004-02-02.
Object id is 3699, canonical name is EgorovsTheorem.
Accessed 7452 times total.

Classification:
AMS MSC28A20 (Measure and integration :: Classical measure theory :: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence)

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