Let ℳ be the Banach space of real measures on a σ -ring R , let ℳ ′ be its dual, let E be a quasi-complete locally convex space, let E ′ be its dual, and let μ be an E -valued measure on R . If is shown that for any θ ∈ ℳ ′ there exists an element ∫ θ d μ of E such that 〈 x ′ ∘ μ , θ 〉 = ∫ θ d μ , x ′ for any x ′ ∈ E ′ and that the map θ → ∫ θ d μ : ℳ ′ → E is order continuous. It follows that the closed convex hull of μ ( R ) is weakly compact.