Question: 1.*16. Strengthen Theorem 4.2.4 by proving that . In hm = 1 a.e. n-+oo g(l n) [HINT: Take a subsequence {kn} such that g(lnk) '

1.*16. Strengthen Theorem 4.2.4 by proving that

. In hm = 1 a.e. n-+oo g(l n)

[HINT: Take a subsequence {kn} such that g(lnk) '" k2 ; prove the result first for this subsequence by estimating 9{lh -cff(lk) I > 8cf(ld}; the general case follows because if n k ::::; n < n k+! ,

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