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...

Full description

Saved in:
Bibliographic Details
Published in:Resultate der Mathematik 2016-11, Vol.70 (3-4), p.349-371
Main Authors: Chiţescu, Ion, Ioana, Loredana, Miculescu, Radu, Niţă, Lucian
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-016-0531-1