Properties of Riesz capacity are developed with respect to the kernel exponent p ∈ (-∞,n), namely that capacity is monotonic as a function of p, that its endpoint limits recover the diameter and volume of the set, and that capacity is left-continuous with respect to p and is right-continuous provided (when p ≥ 0) that an additional hypothesis holds. Left and right continuity properties of the equilibrium measure are obtained too.
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Clark et al. (2024) studied this question.
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