\(L^p\)-continuity of conditional expectations (Q1269569)
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scientific article; zbMATH DE number 1215644
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^p\)-continuity of conditional expectations |
scientific article; zbMATH DE number 1215644 |
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\(L^p\)-continuity of conditional expectations (English)
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2 August 1999
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A necessary and sufficient condition on a sequence \(({\mathcal A}_n)_{n\in\mathbb{N}}\) of \(\sigma\)-subalgebras is given such that the conditional expectations \(E(f\mid {\mathcal A}_n)\) converge in \(L^p\)-norm \((1\leq p<\infty)\). This result generalizes the convergence theorem of the \(L^p\)-martingales, the Fetter and Boylan equi-convergence theorems. Some examples and counterexamples are also given.
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convergence of conditional expectations
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martingales
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