Let (fn ne N) be a sequence of non-negative real-valued measurable functions on R such that...

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Let (fn ne N) be a sequence of non-negative real-valued measurable functions on R such that fn fa.e. on R. → Suppose limn-∞ f fndμ = ffdµ < 0. Show that for each measurable set ECR we have lim n-∞ | fndµ = [ƒdµ. E E Let (fn ne N) be a sequence of non-negative real-valued measurable functions on R such that fn fa.e. on R. → Suppose limn-∞ f fndμ = ffdµ < 0. Show that for each measurable set ECR we have lim n-∞ | fndµ = [ƒdµ. E E

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