7.4. Lebesgue Integral

Definition 7.4.3: Lebesgue Integral for Simple Function

If s(x) = an XAn(x) is a simple function and m(An) is finite for all n, then the Lebesgue Integral of s is defined as
s(x) dx = an m(An)
If E is a measurable set, we define
E s(x) dx = XE(x) s(x) dx
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