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Israel Journal of Mathematics

, Volume 25, Issue 1–2, pp 154–187 | Cite as

Applications of nonstandard analysis to ideal boundaries in potential theory

  • Peter A. Loeb
Article

Abstract

A solution is given of the generalized Dirichlet problem for an arbitrary compactification of a Brelot harmonic space. A method of obtaining the Martin-Choquet integral representation of positive harmonic functions is given, and the existence is established of an ideal boundary Δ supporting the maximal representing measures for positive bounded and quasibounded harmonic functions with almost all points of Δ being regular for the Dirichlet problem.

Keywords

Harmonic Function Dirichlet Problem Potential Theory Harmonic Measure Continuous Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1976

Authors and Affiliations

  • Peter A. Loeb
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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