[For the entire collection see Zbl 0747.00029.]
A Riesz space \(L\) is considered with separating order continuous dual and measurability of elements of the extended order continuous dual \(G(L)\) is defined. This approach is motivated by the measurability of real functions with respect to a \(\delta\)-ring \(D\). If \(A\in D\), \(M(D)\) is the Riesz space of all real-valued functions, then \(\hat f: M(D)\to R\) defined by \(\hat f(m)=\int f dm\), is a member of \(G(M(D))\). The property \(\{f\geq c\}\cap A\in D\) is translated into the language of \(G(L)\) by the representation theory of Riesz spaces. A Radon-Nikodym type theorem is proved.