Given a measure space (X,U, u). Let {fn: ne N} and f be extended real-valued U-measurable functions on a set DEU and let {gn n € N} and g be nonnegative extended real-valued U-measurable functions on D. Suppose : 1° lim fn = f and lim 9n = g a.e. on D, n-x nx 2° {gn ne N} and g are all u-integrable on D and lim / Shudu = 1₁ D 3° fn9n on D for every n E N. Show that f is u-integrable on D and lim/Judu-du. H

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