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Need help with this - just had this on a test and this is driving me crazy - PLEASE HELP!!

Let {[itex]f_{n}[/itex]} be a sequence of MEASURABLE real valued functions. Prove that there exists a sequence of positive real numbers {[itex]c_{n}[/itex]} such that [itex]\sum c_{n}f_{n}[/itex] converges for almost every x [itex]\in[/itex] [itex]\Re[/itex]

How is it possible for this to be true??? Please help!!

Let {[itex]f_{n}[/itex]} be a sequence of MEASURABLE real valued functions. Prove that there exists a sequence of positive real numbers {[itex]c_{n}[/itex]} such that [itex]\sum c_{n}f_{n}[/itex] converges for almost every x [itex]\in[/itex] [itex]\Re[/itex]

How is it possible for this to be true??? Please help!!

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