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March 2001 Jensen measures and boundary values of plurisubharmonic functions
Frank Wikström
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Ark. Mat. 39(1): 181-200 (March 2001). DOI: 10.1007/BF02388798

Abstract

We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic functions in B-regular domain. This theorem implies that the two classes of Jensen measures coincide in B-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above.

The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values of a continuous plurisubharmonic function.

Citation

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Frank Wikström. "Jensen measures and boundary values of plurisubharmonic functions." Ark. Mat. 39 (1) 181 - 200, March 2001. https://doi.org/10.1007/BF02388798

Information

Received: 10 March 1999; Revised: 21 October 1999; Published: March 2001
First available in Project Euclid: 31 January 2017

zbMATH: 1021.32014
MathSciNet: MR1821089
Digital Object Identifier: 10.1007/BF02388798

Rights: 2001 © Institut Mittag-Leffler

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Vol.39 • No. 1 • March 2001
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