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Levy's theorem and strong convergence of martingales in a dual spaceKeywords: s-measurable function, conditional expectation, martingale, mil, Levy's theorem, tightness, sequential weak upper limits, weak-star, weak and strong convergence Abstract: 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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