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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
x
axis). The Lebesgue integral is constructed by partitioning the integrand's co-domain (on the
y
axis). For each value
y
in the co-domain, find the measure
m(y)
of the corresponding set of points
-1
f
(y)
in the domain. Roughly speaking, the Lebesgue integral is then the sum of all the products
ym(y)
.
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