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


Iterated fine limits

Author: Kohur GowriSankaran
Journal: Proc. Amer. Math. Soc. 108 (1990), 157-162
MSC: Primary 31D05
MathSciNet review: 987609
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Abstract: Let $ v$ and $ u$ be, respectively $ n$-superharmonic and $ n$-harmonic functions on the product of $ n$ harmonic spaces. We prove that the iterated fine limits of $ \frac{v}{u}$ exist and are independent of the order, for $ \lambda $ almost every minimal boundary element where $ \lambda $ represents the function $ u$. As an application we prove an important property concerning the reduced function of a positive $ n$-harmonic function.

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PII: S 0002-9939(1990)0987609-5
Keywords: $ n$-superharmonic, fine limits, multi-reduced function
Article copyright: © Copyright 1990 American Mathematical Society