Interactive Real Analysis - part of MathCS.org

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If f is a 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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