Weak almost periodicity of Haar measurable functions (Q802102)

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.