 The concept of a random variable admits several generalizations to the setting of test spaces. Let us agree that a simple (real-valued) random variable on a test space \(\mathcal{A}\) is a mapping \(f : E \rightarrow \mathbf{R}\) where \(E\) is a test in \(\mathcal{A}\). We define the expected value of \(f\) in a state \(\omega \in \Omega(\mathcal{A})\) in the obvious way, namely, as the expected value of \(f\) with respect to the probability weight obtained by restricting \(\omega\) to \(E\) (provided, of course, that this expected value exists). One can go on to define more general classes of random variables by taking suitable limits (for details, see Younce [1987]).