Fatou's lemma and Lebesgue's convergence theorem for measures (Q1580051)
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scientific article; zbMATH DE number 1507626
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fatou's lemma and Lebesgue's convergence theorem for measures |
scientific article; zbMATH DE number 1507626 |
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Fatou's lemma and Lebesgue's convergence theorem for measures (English)
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14 January 2001
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Let \((\mu_n)\) be a sequence of measures and \(f\), \(f_n\) measurable nonnegative functions. The main object of study is the sequence \((\int f d\mu_n)\). More generally, the asymptotic behavior of \((\int f_nd\mu_n)\) is studied. When \((\mu_n)\) converges setwise or weakly, a dominated convergence theorem is obtained. Some applications are presented.
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Fatou lemma
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Lebesgue convergence theorem
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dominated convergence theorem
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