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Levy's theorem and strong convergence of martingales in a dual space

Author(s): M. Saadoune

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXI;
Issue: 1;
Start page: 31;
Date: 2012;
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Keywords: &#115-measurable function | conditional expectation | martingale | mil | Levy's theorem | tightness | sequential weak upper limits | weak-star | weak and strong convergence

We prove Levy's Theorem for a new class of functions taking values in a dual space and we obtain almost sure strong convergence of martingales and mils satisfying various tightness conditions.
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