Weighted capacity and the Choquet integral

Adams, David R.

doi:10.1090/S0002-9939-1988-0934860-7

Weighted capacity and the Choquet integral
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by David R. Adams

Proc. Amer. Math. Soc. 102 (1988), 879-887

DOI: https://doi.org/10.1090/S0002-9939-1988-0934860-7

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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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A note on differentiation with respect to

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