Geodesic
Almost periodic measure-valued functions
Sbornik. Mathematics, Tome 191 (2000) no. 12, pp. 1773-1796
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Weakly almost periodic measure-valued functions $\mathbb R\ni t\to\mu[\,\cdot\,;t]$ taking values in the space $\mathscr M(U)$ of Borel measures of variable sign in a complete separable metric space $U$ are considered. A norm ${\|\cdot\|}_w$ introduced in the space $\mathscr M(U)$ defines a metric on the set of probability Borel measures that is equivalent to the Levy–Prokhorov metric. A connection between the almost periodicity of a measure-valued function $t\to\mu[\,\cdot\,;t]\in (\mathscr M(U),{\|\cdot\|}_w)$ and its weak almost periodicity (both in the sense of Bohr and in the sense of Stepanov) is established. 
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     author = {L. I. Danilov},
     title = {Almost periodic measure-valued functions},
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     volume = {191},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_12_a1/}
}
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L. I. Danilov. Almost periodic measure-valued functions. Sbornik. Mathematics, Tome 191 (2000) no. 12, pp. 1773-1796. http://geodesic.mathdoc.fr/item/SM_2000_191_12_a1/

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