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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On semiregular points of the Martin boundary


Authors: Aurel Cornea and Peter A. Loeb
Journal: Proc. Amer. Math. Soc. 103 (1988), 117-124
MSC: Primary 31D05; Secondary 31C35
MathSciNet review: 938654
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Abstract: For a selfadjoint, Brelot harmonic space with Martin boundary, call "semiregular" a point $ z$ of the boundary at which the Green function has a positive upper limit; call "maximal" the filter $ {\mathcal{F}_z}$ converging to $ z$ along which that upper limit is attained. If such a $ z$ is minimal then any bounded harmonic function has a limit along $ {\mathcal{F}_z}$ and $ {\mathcal{F}_z}$ is coarser than the fine filter associated with $ z$. The semiregular points form a set of harmonic measure zero.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0938654-8
PII: S 0002-9939(1988)0938654-8
Keywords: Martin boundary, Fine neighborhood, harmonic boundary
Article copyright: © Copyright 1988 American Mathematical Society