2014/04/19 by Ion Chițescu, Chitescu, Ion, Radu Miculescu +5
Mathematics · #28C15. Secondary: 46B25 #46C05 #46E10 #46G10 #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Primary: 28B05 #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1404.4980
openalex publication_date 2014/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 functions 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.