Suppose that ( = {(1, (2,...}, and let A be the discrete Ï-field. On A, define the

Suppose that ( = {(1, (2,...}, and let A be the discrete σ-field. On A, define the set function μ by

Then show that
(i) μ is nonnegative, μ(Ø = 0 and is finitely additive, but it is not σ-additive.
(ii) ( = limn†’( An for a sequence {An}, with An ( An+1, n ( 1, and μ (An) = 0 (and therefore μ) (Acn) = (), n ( 1.

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0 if A is finite, 11 (A) if A is infinite. X