Linear functionals on spaces of uniformly continuous functions and abstract measures (Q5902824)

Let X be a complete, Hausdorff, uniform space (LX, \(t_ M)^{\bigwedge}\) the completion of its free locally convex space. Then each positive element of \((LX,t_ M)^{\bigwedge}\) can be represented by an integral with respect to a \(\sigma\)-additive measure on X. For arbitrary elements of \((LX,t_ M)^{\bigwedge}\) this is not necessarily true.