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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
DOI: https://doi.org/10.1090/S0002-9939-1990-0987609-5
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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Keywords: <IMG WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$n$">-superharmonic, fine limits, multi-reduced function
Article copyright: © Copyright 1990 American Mathematical Society