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

 

Weighted capacity and the Choquet integral


Author: David R. Adams
Journal: Proc. Amer. Math. Soc. 102 (1988), 879-887
MSC: Primary 31B15; Secondary 35J99
MathSciNet review: 934860
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Abstract: The capacity set function that is naturally associated with a linear second-order elliptic partial differential operator in divergence form is related to the concept of the Choquet integral of a weight function with respect to Newtonian capacity. The weight function comes from the coefficients of the differential operator. This idea is reminiscent of the Radon-Nikodym Theorem, but now for capacities instead of measures.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0934860-7
PII: S 0002-9939(1988)0934860-7
Article copyright: © Copyright 1988 American Mathematical Society