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arXiv · 1810.09490

On norm almost periodic measures

Timo Spindeler·Nicolae Strungaru
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Abstract

In this paper, we study norm almost periodic measures on locally compact Abelian groups. First, we show that the norm almost periodicity of $\mu$ is equivalent to the equi-Bohr almost periodicity of $\mu*g$ 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.

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Timo Spindeler, Nicolae Strungaru. 2018-10-22. On norm almost periodic measures. https://doi.org/10.1007/s00209-020-02671-w

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