graph of that function and the X axis. The Lebesgue integral, named after French mathematician Henri Lebesgue, is one way to make this concept rigorous...

Riemann integral for the Lebesgue integral. The definition of the Lebesgue integral is not obviously a generalization of the Riemann integral, but it...

early 20th century, Henri Lebesgue generalized Riemann's formulation by introducing what is now referred to as the Lebesgue integral; it is more general than...

measure-theoretic framework. The Lebesgue–Stieltjes integral is the ordinary Lebesgue integral with respect to a measure known as the Lebesgue–Stieltjes measure, which...

aire ("Integral, length, area") at the University of Nancy during 1902. Henri Lebesgue was born on 28 June 1875 in Beauvais, Oise. Lebesgue's father was...

Improper integrals can also be evaluated in the context of complex numbers, in higher dimensions, and in other theoretical frameworks such as Lebesgue integration...

λ(A). Henri Lebesgue described this measure in the year 1901 which, a year after, was followed up by his description of the Lebesgue integral. Both were...

generalization of the Riemann integral, and in some situations is more general than the Lebesgue integral. In particular, a function is Lebesgue integrable over a...

inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The...

definition of the Lebesgue integral for a non-negative function). Remark 4. The proof below does not use any properties of the Lebesgue integral except those...