space ({, F. IF, P) is given. 1. Basic Properties of the Probability Function. Using just the axiomatic properties of the probability function P from its definition, prove: (a) PIO] = 0. (b) If A1, .... Ay are events such that A, n Am = 0,n # m then [UA. = EPIAN This property is called finite additivety. (c) If A1, Am, ... are events, not necessarily such that A, nAm = 0,n / m, then Ntoo lim P UA - PUA.. This property is called continuity of the probability function