Let 2 be a non-empty set. Let Fo be the collection of all subsets such that either A or AC is finite. (a) Show that Fo is a field. Define for E E Fo the set function P by 0, P(E) = { if E is finite, if EC is finite. 1, (b) If S2 is countably infinite, show P is finitely additive but not o-additive. (c) If S2 is uncountable, show P is o-additive on Fo.

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