Lebesgue Integration

Lebesgue integration extends the definition of integral to a much larger class of functions than the class of Riemann integrable functions. The Riemann integral is constructed by partitioning the integrand's domain (on the axis). The Lebesgue integral is constructed by partitioning the integrand's co-domain (on the axis). For each value in the co-domain, find the measure of the corresponding set of points in the domain. Roughly speaking, the Lebesgue integral is then the sum of all the products .

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