On norm almost periodic measures

In this paper, we study norm almost periodic measures on locally compact Abelian groups. First, we show that the norm almost periodicity of μ is equivalent to the equi-Bohr almost periodicity of μ ∗ g for all g in a fixed family of functions. Then, we show that, for absolutely continuous measures, n...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 299; no. 1-2; pp. 233 - 255
Main Authors Spindeler, Timo, Strungaru, Nicolae
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021
Springer Nature B.V
Subjects
Equivalence
Group theory
Mathematics
Mathematics and Statistics
Almost periodic measures
43A25
43A05
Lebesgue decomposition
52C23
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Summary:In this paper, we study norm almost periodic measures on locally compact Abelian groups. First, we show that the norm almost periodicity of μ is equivalent to the equi-Bohr almost periodicity of μ ∗ g for all g in a fixed family of functions. Then, we show that, for absolutely continuous measures, norm almost periodicity is equivalent to the Stepanov almost periodicity of the Radon–Nikodym density.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02671-w