Let {f_{n}}_{n in mathbb {N}} be a sequence of integrable functions on a σ-finite measure space (Omega, mathscr {F}, mu ). Suppose that the pointwise limit lim_{n uparrow infty } f_{n} exists μ-a.e. and is integrable. In this setting we provide necessary and sufficient conditions for the following equality to hold: limn↑∞∫fndμ=∫limn↑∞fndμ.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\lim_{n \\uparrow \\infty } \\int f_{n} \\, d\\mu = \\int \\lim_{n \\uparrow \\infty } f_{n} \\, d\\mu. $$\\end{document}