ACIT4330-Page/content/Definitions/Measure Theory/Lebesgue's Dominated Convergence Theorem.md
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# Definition
Let $g$ be a real function on $X$.
Define $g^{+} = \max \{ g, 0 \}$, $g^{-} = -\min \{ g, 0 \}$.
Then $g = g^{+} - g^{-}$ and $g^{\pm} \geq 0$.
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