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INTEGRAL REPRESENTATION FOR MULTIPLY SUPERHARMONIC FUNCTIONS
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INTEGRAL REPRESENTATION FOR MULTIPLY SUPERHARMONIC FUNCTIONS
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INTEGRAL REPRESENTATION FOR MULTIPLY SUPERHARMONIC FUNCTIONS
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Dissertation
INTEGRAL REPRESENTATION FOR MULTIPLY SUPERHARMONIC FUNCTIONS
1972
Overview
For i=1,..., n, let ; be a harmonic space of Brelot (viz. i + + satisfying Axioms I, II, III, IV) with positive potential. Let MM-M + where Mis the cone of positive multiply superharmonic functions n on 2 = ΠΩ, An Hausdorff locally convex topology y is defined on i=1 i + M and it is shown that Mhas a compact metrizable base A with respect to y. Thus there is an integral representation for the ele- ments of M in terms of a signed Radon measure on A, carried by the extreme points of A.Some results for tensor products of general ordered Hausdorff locally convex topological vector spaces are given. One of these results is applied in another approach to integral representation for the elements of M which involves duality theory.Finally the nature of the extreme points of the base A is dis- cussed.
