 Then, Pr is a \(\sigma\)- or countably additive probability measure on \(\mathbf{A}\) (Kolmogorov 1956, ch. 2, actually gives a different but equivalent definition; see e.g. Huber 2007a, sct. 4.1). In this case \(\langle W, \mathbf{A}, \Pr\rangle\) is a \(\sigma\)- or countably additive probability space.