Topological vector spaces of Bochner measurable functions
The authors introduce the notion of a topological vector space of Bochner measurable functions defined on a submeasure space and taking their values in a complete metrizable topological vector space. This general notion provides a framework where, as shown in the paper, many familiar results from the theory of Banach lattices, topological Riesz spaces and Lebesgue-Bochner spaces remain true. Among the many interesting results given in this paper, we will mention just a few; namely, the characterizations of Lebesgue and Levi type properties; the characterizations of topological, sequential, and monotone completeness; Orlicz-Pettis type theorems; and the inclusion of copies of \(c_0\) and \(\ell^\infty\).
scientific article; zbMATH DE number 1839947