Topological Properties of the Complex Vector Lattice of Bounded Measurable Functions

Marian Nowak
2013 Journal of Function Spaces and Applications  
Let Σ be aσ-algebra of subsets of a nonempty set Ω. Let be the complex vector lattice of bounded Σ-measurable complex-valued functions on Ω and let be the Banach space of all bounded countably additive complex-valued measures on Ω. We study locally solid topologies on . In particular, it is shown that the Mackey topology is the finest locally convex-solidσ-Lebesgue topology on .
doi:10.1155/2013/343685 fatcat:7e3lew33qjd5xdnspmxvbjlmte