Uniform s-Boundedness and Convergence Results for Measures with Values in Complete l-Groups

Absolute continuity, s-boundedness, and extensions are studied, in the context of the so-called RD-convergence, for set functions taking values in Dedekind complete l-groups. Subsequently, we obtain results of uniform s-boundedness for RD-convergent sequences of measures (Vitali–Hahn–Saks–Nikod´ym theorem) and deduce a Schur-type theorem for measures defined on ∗ .