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Weak almost periodicity of Haar measurable functions. (English) Zbl 0553.43003

Let \(G\) be a locally compact group. A weakened version of Grothendieck’s double limit criterion is shown to characterize those \(\phi\in {\mathcal L}^{\infty}(G)\) that are locally almost everywhere equal to a continuous weakly almost periodic function. Additional measure theoretic conditions guarantee continuity of such \(\phi\). As a by-product, we obtain a short proof of the classical result that \(\phi\) is continuous when almost periodic.
Reviewer: Dietrich Helmer

MSC:

43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
22D05 General properties and structure of locally compact groups
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References:

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