Iterated fine limits
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 by Kohur GowriSankaran PDF
 Proc. Amer. Math. Soc. 108 (1990), 157162 Request permission
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.References

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 Kohur Gowrisankaran, Multiply harmonic functions, Nagoya Math. J. 28 (1966), 27–48. MR 209513
 Kohur Gowrisankaran, Iterated fine limits and iterated nontangential limits, Trans. Amer. Math. Soc. 173 (1972), 71–92. MR 311927, DOI 10.1090/S00029947197203119270
 Laurent Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Tata Institute of Fundamental Research Studies in Mathematics, No. 6, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1973. MR 0426084
Additional Information
 © Copyright 1990 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 108 (1990), 157162
 MSC: Primary 31D05
 DOI: https://doi.org/10.1090/S00029939199009876095
 MathSciNet review: 987609