Let (fn) be a sequence of extended real-valued measurable functions on X and let f be...

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Let (fn) be a sequence of extended real-valued measurable functions on X and let f be an extended real-valued function which is finite a.e. on X. Suppose limn- fn = fa.e. on X. Let a = [0, (X)) be arbitrarily chosen. Show that for every > 0 there exists NEN such that µ{X: fn - f\ < } ≥ a for n > N. Let (fn) be a sequence of extended real-valued measurable functions on X and let f be an extended real-valued function which is finite a.e. on X. Suppose limn- fn = fa.e. on X. Let a = [0, (X)) be arbitrarily chosen. Show that for every > 0 there exists NEN such that µ{X: fn - f\ < } ≥ a for n > N.

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