Let An( ) be the event that |Xn ? X| > , and let A( ) be
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Let An( ) be the event that |Xn ? X| > , and let A( ) be the event that infinitely many of (An( ); n ? 1) occur, where >
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Let An( ) be the event that |Xn ? X| > , and let A( ) be the event that infinitely many of (An( ); n ? 1) occur, where > 0. Prove Lemma (6), that Xn ?? a.s. X if, for all > 0, |Xn ? X| > only finitely often. [Hint: P(Xn ? X) = P( >0 A( )) = P( ? m=1 A(m?1)).]
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