If $f_n\to f$ almost everywhere and $\abs{f_n}\le g$ for one $g\in L^1$, then $\int f_n\to\int f$.Suggest a slogan
Let \((X,\mcm,\mu)\) be a measure space, and let \(f_n\colon X\to\CC\) for \(n\geq1\) and \(f\colon X\to\CC\) be measurable. Suppose \(f_n\to f\) almost everywhere and there exists \(g \in L^1(X,\mu)\) with \(\abs{f_n} \leq g\) almost everywhere for every \(n\). Then \(f\in L^1(X,\mu)\) and \[ \lim_{n\to\infty} \int_X f_n\dmu = \int_X f\dmu . \]
State the dominated convergence theorem.