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


Author: Leonid G. Hanin
Journal: Proc. Amer. Math. Soc. 115 (1992), 345-352
MSC: Primary 46E15; Secondary 28A33, 46E27, 54C30, 54E45
DOI: https://doi.org/10.1090/S0002-9939-1992-1097344-5
MathSciNet review: 1097344
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1097344-5
Keywords: Kantorovich-Rubinstein norm, Lipschitz space, completion, isometric isomorphism
Article copyright: © Copyright 1992 American Mathematical Society

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