Abstract
Let K be a compact set in a Euclidean space and let d be a metric on K which is continuous with respect to the usual topology. The generalized energy integral I(μ) = ff d(x, y) dμ(x) dμ{y) is investigated as μ is allowed to range over the lamily of signed Borel measures of total mass one concentrated on K. A trick of integral geometry is used to define a class of metrics d, including many standard ones, possessing a number of pleasing properties related to the functional /.
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