p. 31 - 54 Levy's theorem and strong convergence of martingales in a dual space M. Saadoune Received: February 24, 2011; Revised: June 6, 2011; Accepted: June 21, 2011 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. Keywords: s-measurable function; conditional expectation; martingale; mil; Levy's theorem; tightness; sequential weak upper limits; weak-star; weak and strong convergence AMS Subject classification: Primary: 60B11, 60B12, 60G48 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2012, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |