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Slices, RNP, strong regularity, and martingales

Published online by Cambridge University Press:  17 April 2009

Maria Girardi  and
J.J. Uhl Jr
Maria Girardi
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green St, Urbana, IL 61801, United States of America
J.J. Uhl Jr
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green St, Urbana, IL 61801, United States of America
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The usual proof that dentability implies the Radon-Nikodým property involves a clever but rather baroque exhaustion argument. This note presents a very short and simple proof of this implication. The techniques in this new proof are then generalised to derive some direct proofs of recent results concerning strongly regular operators on L1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 411 - 415
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bourgain, J., ‘Dunford-Pettis operators on L 1 and the Radon-Nikodým property’, Israel J. Math. 37 (1980), 34–47.CrossRefGoogle Scholar
[2]Diestel, J. and Uhl, J. J. Jr., Vector Measures, Math. Surveys, no. 15 (American Mathethematical Society, Providence, R.I., 1977).CrossRefGoogle Scholar
[3]Ghoussoub, N., Godefroy, G., Maurey, B., and Schachermayer, W., ‘Some topological and geometrical structures in Banach spaces’, in Mem. American Mathematical Society, 70, no. 378 (Amer. Math. Soc., Providence, R.I., 1987).Google Scholar