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Izv. IMI UdGU, 2005, Issue 1(31), Pages 79–98 (Mi iimi85)  

This article is cited in 2 scientific papers (total in 2 papers)

On Weyl almost periodic measure-valued functions

L. I. Danilov

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Abstract: We consider measure-valued functions ${\mathbb{R}}\ni t\to \mu [.;t]$ taking values in the metric space $({\mathcal M}_0(U),\rho _w)$ of probability Borel measures defined on the $\sigma$-algebra of Borel subsets of a complete seperable metric space $U$. The metric space $({\mathcal M}_0(U), \rho _w)$ is endowed with the metric $\rho _w$ equivalent to the Lévy–Prokhorov metric. It is proved that the measure-valued function ${\mathbb{R}}\ni t\to \mu  [ . ;t]\in ({\mathcal M}_0(U),\rho _w)$ is Weyl almost periodic if and only if the functions $\int\limits_U{\mathcal F}(x)  \mu  [ dx; . ]$ are Weyl almost periodic (of order 1) for all bounded continuous functions ${\mathcal F}:U\to {\mathbb{R}}$.

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UDC: 517.9

Citation: L. I. Danilov, “On Weyl almost periodic measure-valued functions”, Izv. IMI UdGU, 2005, no. 1(31), 79–98

Citation in format AMSBIB
\Bibitem{Dan05}
\by L.~I.~Danilov
\paper On Weyl almost periodic measure-valued functions
\jour Izv. IMI UdGU
\yr 2005
\issue 1(31)
\pages 79--98
\mathnet{http://mi.mathnet.ru/iimi85}


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    This publication is cited in the following articles:
    1. L. I. Danilov, “Pochti periodicheskie po Veilyu secheniya nositelei meroznachnykh funktsii”, Sib. elektron. matem. izv., 3 (2006), 384–392  mathnet  mathscinet  zmath
    2. L. I. Danilov, “Pochti periodicheskie po Veilyu secheniya mnogoznachnykh otobrazhenii”, Izv. IMI UdGU, 2006, no. 3(37), 27–28  mathnet
  • Известия Института математики и информатики Удмуртского государственного университета
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