Lebesgue integration

In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the x-axis. The Lebesgue integral extends the integral to a larger class of functions. It also extends the domains on which these functions can be defined. The Lebesgue integral plays an important role in probability theory, real analysis, and many other fields in mathematics. It is named after Henri Lebesgue (1875–1941), who introduced the integral . It is also a pivotal part of the axiomatic theory of probability.

Lebesgue integration

In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the x-axis. The Lebesgue integral extends the integral to a larger class of functions. It also extends the domains on which these functions can be defined. The Lebesgue integral plays an important role in probability theory, real analysis, and many other fields in mathematics. It is named after Henri Lebesgue (1875–1941), who introduced the integral . It is also a pivotal part of the axiomatic theory of probability.