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Measurable function

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Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x.

Please make sure to show the proof in both directions.

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Solution Summary

It shows that a function f is measurable if and only if there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x. The solution shows the proof in both directions. The response is detailed and well presented.

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Show that a function f is measurable IF AND ONLY IF there exists a ...

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