Let f be a real-valued Lebesgue measurable function on [0, ) such that 1. f is...

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Let f be a real-valued Lebesgue measurable function on [0, ∞) such that 1. f is Lebesgue integrable on every finite subinterval of [0, ∞). 2. lim f(x) = c E R. Show that 1 lim a-∞ a [0,a] fdμL = c. Let f be a real-valued Lebesgue measurable function on [0, ∞) such that 1. f is Lebesgue integrable on every finite subinterval of [0, ∞). 2. lim f(x) = c E R. Show that 1 lim a-∞ a [0,a] fdμL = c.

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