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

Bu, Shang Quan; Schachermayer, Walter

doi:10.1090/S0002-9947-1992-1035999-6

Approximation of Jensen measures by image measures under holomorphic functions and applications
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by Shang Quan Bu and Walter Schachermayer PDF

Trans. Amer. Math. Soc. 331 (1992), 585-608 Request permission

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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