term Lebesgue integration can mean either the general theory of integration of a function with respect to a general measure, as introduced by Lebesgue, or...

related branches of mathematics, Lebesgue–Stieltjes integration generalizes both Riemann–Stieltjes and Lebesgue integration, preserving the many advantages...

theorem of calculus or approximated by numerical integration, or simulated using Monte Carlo integration. Let f be a non-negative real-valued function on...

mathematics, Lebesgue integrability may refer to: Whether the Lebesgue integral of a function is defined; this is what is most often meant. The Lebesgue integrability...

Léon Lebesgue ForMemRS (French: [ɑ̃ʁi leɔ̃ ləbɛɡ]; June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which...

functions are Lebesgue-integrable. Integrals may be generalized depending on the type of the function as well as the domain over which the integration is performed...

particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called Lebesgue-measurable; the measure of the Lebesgue-measurable set...

utility are two of the primary theoretical advantages of Lebesgue integration over Riemann integration. In addition to its frequent appearance in mathematical...

calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of...

function w on X such that for every Lebesgue integrable function f : Y → R, the function (f ∘ φ) ⋅ w is Lebesgue integrable on X, and ∫ Y f ( y ) d ρ ( y )...