The field contains all open and closed intervals, all points, and, in fact, every set of points on the real line that is of interest in the applications. One might wonder whether f does not include all subsets of F. Actually, it is possible to show that there exist sets of points on the real line that are not countable unions and intersections of intervals. Such sets, however, are of no interest in most applications. To complete the specification of F, it suffices to assign probabilities to the events {x £ xi}. All probabilities can then be determined from the axioms.

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