7.4. Lebesgue Integral

Definition 7.4.16: Lebesgue Integral of Non-Negative Functions

If f is a non-negative measurable function defined on E and h is a bounded measurable function such that m( {x: h(x) # 0} ) is finite, then we define
E f(x) dx = sup{ E h(x) dx, h f }
If E f(x) dx is finite, then f is called Lebesgue integrable over E.
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