Kantorovich-Rubinstein norm and its application in the theory of Lipschitz spaces

Hanin, Leonid G.

doi:10.1090/S0002-9939-1992-1097344-5

Kantorovich-Rubinstein norm and its application in the theory of Lipschitz spaces
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Proc. Amer. Math. Soc. 115 (1992), 345-352 Request permission

Abstract:

We obtain necessary and sufficient conditions on a compact metric space $\left ( {K,\rho } \right )$ that provide a natural isometric isomorphism between completion of the space of Borel measures on $K$ with the Kantorovich-Rubinstein norm and the space ${( {\operatorname {lip}( {K,\rho } )} )^*}$ or equivalently between the spaces $\operatorname {Lip}( {K,\rho } )$ and ${( {\operatorname {lip}( {K,\rho } )} )^{**}}$. Such metric spaces are studied and related properties of Lipschitz spaces are established.

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