Uniform exhaustivity and Banach lattices
The measure theoretic notion of strong boundedness is extended to the setting of a real \(\sigma\)-complete Banach lattice X; the lattice theoretic concept which corresponds to strong boundedness is termed exhaustivity. Uniformly exhaustive subsets of X are studied, and various characterizations are presented. One of these characterizations involves the order continuity of the norm on X. The exhaustive elements of certain classical lattices are cataloged. Applications are given to spaces of measures.
scientific article; zbMATH DE number 4015446