A primal representation of the Monge-Kantorovich norm

Abstract: In this note, following \cite{Chitescuetal2014}, we show that the Monge-Kantorovich norm on the vector space of countably additive measures on a compact metric space has a primal representation analogous to the Hanin norm, meaning that similarly to the Hanin norm, the Monge-Kantorovich norm can be seen as an extension of the Kantorovich-Rubinstein norm from the vector subspace of zero-charge measures, implying a number of novel results, such as the equivalence of the Monge-Kantorovich and Hanin norms.