On the \(L^ 1_{{\mathcal F}}\) convergence for conditional Amarts (Q1105907)
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scientific article; zbMATH DE number 4060431
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(L^ 1_{{\mathcal F}}\) convergence for conditional Amarts |
scientific article; zbMATH DE number 4060431 |
Statements
On the \(L^ 1_{{\mathcal F}}\) convergence for conditional Amarts (English)
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1988
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In this note we develop the relation between another type of conditional convergence of a sequence of random variables. Moreover, we generalise the theorem of convergence in \(L^ 1\) for amarts. An interesting result is stated in Theorem 4: Every uniformly \({\mathcal F}\)-integrable conditional amart converges a.s. and in \(L^ 1_{{\mathcal F}}\).
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semiamart
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amart
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conditional convergence of a sequence of random variables
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conditional amart
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