2.1.2 Introduction of Probability
Having dealt with the space of events we can now introduce the notion of
probability. To each event A in the space of events B we assign a real number P.A/,
the probability of A. This assignment has to satisfy the following properties:
• P.A/ 0 for all A 2 B,
• P.˝/ D 1,
• LetAi ; i D 1; : : : be countably many (i.e. possibly infinitely many) disjoint sets
in B with Ai Aj D ;for i ¤ j , then