Problem 1493 (difficulty: 4/10)

Show using the Beppo Levi's theorem that if \(\displaystyle f_n\) is non-negative and \(\displaystyle \mu\)-measurable on a \(\displaystyle \mu\)-measurable set \(\displaystyle A\) and \(\displaystyle \int_A f_nd\mu<1/n^2\), then \(\displaystyle f_n\to 0\) \(\displaystyle \mu\)-a.e.

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