The authors study measures defined on an algebra of sets with values in a weakly \(\sigma\)-distributive Dedekind complete \(l\)-group. They first give an extension theorem for \(\sigma\)-additive measures from an algebra to the generated \(\sigma\)-algebra. The extension theorem is used in the proof of other theorems to reduce the finitely-additive case to the \(\sigma\)-additive case with the aid of a Stone space argument. The paper contains a Lebesgue decomposition theorem and a Vitali-Hahn-Saks theorem. The main theorem contains a statement of the following type: If \(m_n\) are measures converging pointwise to \(m\) and if \(m_n= m^a_n+ m^s_n\) and \(m=m^a+m^s\) are the Lebesgue decompositions, respectively, of \(m_n\) and \(m\) into the absolutely continuous and singular parts with respect to a real-valued positive measure, then \(m^a_n\) and \(m^s_n\) converge pointwise to \(m^a\) and \(m^s\), respectively.