Topological properties of the complex vector lattice of bounded finitely additive mesures

Let $\mathrm{\Sigma }$ be a $\sigma$-algebra of subsets of a non-empty set $\mathrm{\Omega }$. Let $ba(\mathrm{\Sigma })$ be the complex vector lattice of bounded finitely additive measures $\mu :\mathrm{\Sigma }\to \mathbb{C}$. We study locally solid topologies on $ba(\mathrm{\Sigma })$. We develop the duality theory of $ba(\mathrm{\Sigma })$, provided with locally convex-solid topologies.