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Jensen measures and boundary values of plurisubharmonic functions

Frank Wikström Department of Mathematics, Umeå University

TBD mathscidoc:1701.332959

Arkiv for Matematik, 39, (1), 181-200, 1999.3
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.
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@inproceedings{frank1999jensen,
  title={Jensen measures and boundary values of plurisubharmonic functions},
  author={Frank Wikström},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203601633111768},
  booktitle={Arkiv for Matematik},
  volume={39},
  number={1},
  pages={181-200},
  year={1999},
}
Frank Wikström. Jensen measures and boundary values of plurisubharmonic functions. 1999. Vol. 39. In Arkiv for Matematik. pp.181-200. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203601633111768.
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