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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Approximation of Jensen measures by image measures under holomorphic functions and applications

Authors: Shang Quan Bu and Walter Schachermayer
Journal: Trans. Amer. Math. Soc. 331 (1992), 585-608
MSC: Primary 46G10; Secondary 46B22, 60G46
MathSciNet review: 1035999
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Abstract: We show that Jensen measures defined on $ {\mathbb{C}^n}$ or more generally on a complex Banach space $ X$ can be approximated by the image of Lebesgue measure on the torus under $ X$-valued polynomials defined on $ \mathbb{C}$. We give similar characterizations for Jensen measures in terms of analytic martingales and Hardy martingales. The results are applied to approximate plurisubharmonic martingales by Hardy martingales, which enables us to give a characterization of the analytic Radon-Nikodym property of Banach spaces in terms of convergence of plurisubharmonic martingales, thus solving a problem of G. A. Edgar.

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Keywords: Plurisubharmonic martingales, Hardy martingales, Jensen measures, the analytic Radon-Nikodym property
Article copyright: © Copyright 1992 American Mathematical Society