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Let $\{f_n\}$ be a sequence of non-negative measurable functions such that $f_n$ converges to $f$ and $ f_n \le f $ for each $n$, prove that $\lim_{n\to \infty} $ $\int f_n = \int f$

any hints will be appreciated, I thought I could use MCT but didn't know how to apply iy

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The statement of monotone convergence theorem is: "If $\{f_n\}$ is a sequence of non-negative measurable functions such that $f_n \leq f_{n+1}$ for all $n$ and $f = \lim_{n \to \infty} f_n$, then $\int f = \lim_{n \to \infty} f$."

Can you form an increasing sequence of functions from $\{f_n\}$ which increases pointwise to $f$? (Hint: use sup).

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