Definition 7.4.16: Lebesgue Integral of Non-Negative Functions
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.