A. s. convergence of two-parameter Banach space valued martingales and the Radon-Nikodym property of Banach spaces (Q1292795)
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scientific article; zbMATH DE number 1321984
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A. s. convergence of two-parameter Banach space valued martingales and the Radon-Nikodym property of Banach spaces |
scientific article; zbMATH DE number 1321984 |
Statements
A. s. convergence of two-parameter Banach space valued martingales and the Radon-Nikodym property of Banach spaces (English)
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7 June 2000
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Two-parameter martingales with values in Banach spaces are studied. Martingale characterizations of so called \(F_4\) and the local \(F_4\) conditions are given. It is also proved that under the local \(F_4\) condition any \(L\log^+L\) bounded two-parameter martingale with values in a Banach space \(E\) converges almost surely to an integrable \(E\)-valued random element if and only if the space \(E\) has the Radon-Nikodym property.
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two-parameter martingale
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almost sure convergence
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Radon-Nikodym property
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\(F_4\) condition
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