Let (X, A, ) be a measure space and let (fn)neN, and f, g be extended...

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Let (X, A, μ) be a measure space and let (fn)neN, and f, g be extended real-valued A-measurable and integrable functions on DE A. Suppose that 1. limn-∞ fn = fa.e. on D. 2. limno fp fndu = fpfdu. 3. either fng on D for all n N or fn ≤g on D for all n E N. Show that, for every EEA and ECD, we have limm / Sadje - fdp. = S n-x E E Let (X, A, μ) be a measure space and let (fn)neN, and f, g be extended real-valued A-measurable and integrable functions on DE A. Suppose that 1. limn-∞ fn = fa.e. on D. 2. limno fp fndu = fpfdu. 3. either fng on D for all n N or fn ≤g on D for all n E N. Show that, for every EEA and ECD, we have limm / Sadje - fdp. = S n-x E E

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