(a) An event space F must contain the empty set ∅ and the whole set . This holds as follows. By (1.2), there exists some A ∈ F . By (1.3), Ac ∈ F .We set A1 = A, Ai = Ac for i ≥ 2 in (1.4), and deduce that F contains the union  = A ∪ Ac. By (1.3) again, the complement  \  = ∅ lies in F also.

(b) An event space is closed under the operation of finite unions, as follows. Let A1, A2, . . . , Am ∈ F , and set Ai = ∅ for i > m. Then A :=

Sm i=1 Ai satisfies A =

S

∞i

=1 Ai , so that A ∈ F by (1.4).