Lebesgue Integral of a nonnegative function part I

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At about 34:45, the proof of monotonicity is incorrect! We didn't prove linearity of the Lebesgue integral for nonnegative functions with negative scalars, as this is problematic and creates a possible "infinity - infinity" situation.

The correct proof is simply using the definition! This is a good HW exercise. See Royden's book p. 81 for an outline.

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