To construct a probability space on the real line, we shall considered as sets of points on the real lien. It can be shown that it is impossible to define probabilities to all subsets of F so as to satisfy the axioms. To construct a probability space on the real line, we shall consider as events all intervals x1 £ x £ x2 and their countable unions and intersections. These events from a field f, which is defined as follows.

---