Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions

Abstract EN

Let Σ be a σ-algebra of subsets of a nonempty set Ω.

Let BΣ be the complex vector lattice of bounded Σ-measurable complex-valued functions on Ω and let caΣ be the Banach space of all bounded countably additive complex-valued measures on Ω.

We study locally solid topologies on BΣ.

In particular, it is shown that the Mackey topology τBΣ,caΣ is the finest locally convex-solid σ-Lebesgue topology on BΣ.