Abstract:We propose a family of extensions of the Kantorovich-Rubinstein norm from the space of zero-charge countably additive measures on a compact metric space to the space of all countably additive measures, and a family of extensions of the Lipschitz norm from the quotient space of Lipschitz functions on a compact metric space to the space of all Lipschitz functions. These families are parameterized by p, q ∈ [1, ∞], and if p, q are Hölder conjugates, then the dual of the resulting p-Kantorovich space is isometrica… Show more
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