For an almost everywhere increasing sequence in $L^+$, the integral of the limit is the limit of the integrals.Suggest a slogan
Let \((X,\mcm,\mu)\) be a measure space, and let \(f_n\) for \(n\geq1\) and \(f\) belong to $L^+$. If \(f_n\le f_{n+1}\) almost everywhere for every \(n\) and \(f_n\to f\) almost everywhere, then \[ \lim_{n\to\infty} \int_X f_n \dmu = \int_X f \dmu . \]
State the monotone convergence theorem.