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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