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


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.


Harmonic Function Dirichlet Problem Potential Theory Harmonic Measure Continuous Extension 
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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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