Let (X, A, u) be a measure space and let p = [1, ). Let (fn)neN...

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Let (X, A, u) be a measure space and let p = [1, ∞). Let (fn)neN C LP(X) and fe LP(X) be such that limn-fn- fp = 0. Let (gn)neN be a sequence of complex-valued measurable functions on X such that gn M for every n EN and let g be a complex-valued measurable function on X such that limno In = 9 a.e. on X. Show that limfn9n 71-00 - fgp = 0. Let (X, A, u) be a measure space and let p = [1, ∞). Let (fn)neN C LP(X) and fe LP(X) be such that limn-fn- fp = 0. Let (gn)neN be a sequence of complex-valued measurable functions on X such that gn M for every n EN and let g be a complex-valued measurable function on X such that limno In = 9 a.e. on X. Show that limfn9n 71-00 - fgp = 0.

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