Lebesgue Integration

number of measure sets

16

integrand

x

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)

.

External Links

Lebesgue Integral (Wolfram MathWorld)

Measure (Wolfram MathWorld)

Permanent Citation

Anton Antonov

"Lebesgue Integration"
http://demonstrations.wolfram.com/LebesgueIntegration/
Wolfram Demonstrations Project
Published: June 27, 2007