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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Best filters for the general Fatou boundary limit theorem
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by Jürgen Bliedtner and Peter A. Loeb PDF
Proc. Amer. Math. Soc. 123 (1995), 459-463 Request permission

Abstract:

Given a suitable normalization, there is a "best" family of filters for which the Fatou Boundary Limit Theorem holds. The normalization assigns to each positive harmonic function a set of boundary points at which that function must vanish. Known limits, such as those provided by the Lebesgue Differentiation Theorem, are used to force consistency in this assignment. The zero sets, in turn, are used in constructing the coarsest filters which produce those limits almost everywhere. This procedure is formulated in terms of a general potential theoretic setting and a general reference measure. The result is new, however, even for harmonic functions on the unit disk.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 459-463
  • MSC: Primary 31B25; Secondary 31D05
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1219720-2
  • MathSciNet review: 1219720