=+

(a) Suppose that (2, 7, u) has no "infinite atoms," in the sense that for every A in $, if ( A) = , then there is in F a B such that BCA and 0 < p(B)<0.

Show that if § does not contain an uncountable, disjoint collection of sets of positive measure, then u is o-finite. (Use Zorn's lemma.)