Determining bore-cantelli lemma

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Reference no: EM13127388

Let {f_n} be a sequence of measurable functions on [0,1] with |f_n (x)| < infinity for a.e x. Show that there exists a sequence c_n of positive real numbers such that f_n (x) / c_n -------> 0 a.e.x

Hint: Pick c_n such that m ({x : |f_n (x) / c_n| > 1/n} ) < 2^(-n), and apply the Bore-Cantelli Lemma

Reference no: EM13127388

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