Monge–Kantorovich Norms on Spaces of Vector Measures

One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued measures is defined. Using this integral, different norms (we called them Monge–Kantorovich norm, modified...

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Published in:Resultate der Mathematik 2016-11, Vol.70 (3-4), p.349-371
Main Authors: Chiţescu, Ion, Ioana, Loredana, Miculescu, Radu, Niţă, Lucian
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Mathematics and Statistics
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description One considers Hilbert space valued measures on the Borel sets of a compact metric space. A natural numerical valued integral of vector valued continuous functions with respect to vector valued measures is defined. Using this integral, different norms (we called them Monge–Kantorovich norm, modified Monge–Kantorovich norm and Hanin norm) on the space of measures are introduced, generalizing the theory of (weak) convergence for probability measures on metric spaces. These norms introduce new (equivalent) metrics on the initial compact metric space.
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title Monge–Kantorovich Norms on Spaces of Vector Measures
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