Problem 1488 (difficulty: 5/10)

True or false? If \(\displaystyle f_n\) is non-negative and \(\displaystyle \mu\)-measurable on a \(\displaystyle \mu\)-measurable set \(\displaystyle A\) and \(\displaystyle \int_A f_nd\mu<1/n\) then \(\displaystyle f_n\to 0\) \(\displaystyle \mu\)-a.e.

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