On a generalization of Egoroff's theorem (Q2717465)
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scientific article; zbMATH DE number 1605050
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a generalization of Egoroff's theorem |
scientific article; zbMATH DE number 1605050 |
Statements
14 August 2001
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Egoroff's theorem
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uniform convergence
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On a generalization of Egoroff's theorem (English)
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Standard techniques are used to prove a slight variation of Egoroff's theorem, namely that if a sequence \(\{f_n\}\) of measurable real valued functions converges on a set \(A\), then the sequence converges almost uniformly on any subset \(B \subseteq A\) of finite measure. A standard example showing the need for finiteness of the measure of \(B\) is presented as well.
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