On the pointwise maximum theorem for the almost periodic case (Q1897950)

``The present article is devoted to the investigation of pointwise maximum properties with respect to \(u\in U\in\text{comp}(\mathbb{R}^n)\) of a mapping \((t,u)\mapsto g(t,u)\in\mathbb{R}\), \((t,u)\in\mathbb{R}\times U\), which is almost periodic with respect to \(t\) uniformly in Bohr's sense by \(u\in U\). A similar question is considered in the class of measures as well. These properties play an important role in the investigation of optimal control problems for almost periodic motions and possess a number of specific facilities''.