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Integral representation for a class of multiply superharmonic functions

Kohur Gowrisankaran (1973)

Annales de l'institut Fourier

Let Ω 1 , ... , Ω n be harmonic spaces of Brelot with countable base of completely determining domains. The elements of a subcone C of the cone of positive n -superharmonic functions in Ω 1 × ... × Ω n is shown to have an integral representation with the aid of Radon measures on the extreme elements belonging to a compact base of C . The extreme elements are shown to be the product of extreme superharmonic functions on the component spaces and the measure representing each element is shown to be unique. Necessary and sufficient...

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