=+

(b) Show that discrete spaces are essentially the only ones where this equiva-

lence holds: Suppose that P has a nonatomic part in the sense that there is a set A such that P(A) > 0 and P(LA) is nonatomic. Construct random variables X ,, such that X ,, - +p 0 but X ,, does not converge to 0 with probabil-

ity 1.