1.6. Prove that .q'){ISn I > cp(l -8, sn)i.o.} = 1, without use of (8), as follows. Let ek = {w: ISnk (w)1

h = {W:Sn .. , (w) -Sn,(w) > I'

(1 -~,Sn'+') }.

Show that for sufficiently large k the event ek n f k implies the complement of ek+ 1; hence deduce

and show that the product -+ 0 as k -+ 00.

* (o) = j=jo e; P(e ; ) [ [ [ 1 = P({ })} j=jo