Category: Definitions of mathematical integration

Burkill integral
In mathematics, the Burkill integral is an integral introduced by Burkill for calculating areas. It is a special case of the Kolmogorov integral.
Bochner integral
In mathematics, the Bochner integral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions that take values in a Banach space, as the limit of integrals of simple functi
Motivic integration
Motivic integration is a notion in algebraic geometry that was introduced by Maxim Kontsevich in 1995 and was developed by Jan Denef and François Loeser. Since its introduction it has proved to be qui
Kolmogorov integral
In mathematics, the Kolmogorov integral (or Kolmogoroff integral) is a generalized integral introduced by Kolmogoroff including the Lebesgue–Stieltjes integral, the Burkill integral, and the Hellinger
Stochastic calculus
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to s
Stratonovich integral
In stochastic processes, the Stratonovich integral (developed simultaneously by Ruslan Stratonovich and ) is a stochastic integral, the most common alternative to the Itô integral. Although the Itô in
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
Daniell integral
In mathematics, the Daniell integral is a type of integration that generalizes the concept of more elementary versions such as the Riemann integral to which students are typically first introduced. On
Itô calculus
Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and st
Russo–Vallois integral
In mathematical analysis, the Russo–Vallois integral is an extension to stochastic processes of the classical Riemann–Stieltjes integral for suitable functions and . The idea is to replace the derivat
Sugeno integral
In mathematics, the Sugeno integral, named after M. Sugeno, is a type of integral with respect to a fuzzy measure. Let be a measurable space and let be an -measurable function. The Sugeno integral ove
Hellinger integral
In mathematics, the Hellinger integral is an integral introduced by Hellinger that is a special case of the Kolmogorov integral. It is used to define the Hellinger distance in probability theory.
Henstock–Kurzweil integral
In mathematics, the Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced [dɑ̃ˈʒwa]), Luzin integral or Perron integral,
Riemann integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It was presented
Regulated integral
In mathematics, the regulated integral is a definition of integration for regulated functions, which are defined to be uniform limits of step functions. The use of the regulated integral instead of th
McShane integral
In the branch of mathematics known as integration theory, the McShane integral, created by Edward J. McShane, is a modification of the Henstock-Kurzweil integral. The McShane integral is equivalent to
Homological integration
In the mathematical fields of differential geometry and geometric measure theory, homological integration or geometric integration is a method for extending the notion of the integral to manifolds. Ra
Darboux integral
In the branch of mathematics known as real analysis, the Darboux integral is constructed using Darboux sums and is one possible definition of the integral of a function. Darboux integrals are equivale
Khinchin integral
In mathematics, the Khinchin integral (sometimes spelled Khintchine integral), also known as the Denjoy–Khinchin integral, generalized Denjoy integral or wide Denjoy integral, is one of a number of de
Lebesgue–Stieltjes integration
In measure-theoretic analysis and related branches of mathematics, Lebesgue–Stieltjes integration generalizes both Riemann–Stieltjes and Lebesgue integration, preserving the many advantages of the for
Choquet integral
A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical mechanics and potential theory, but foun
Skorokhod integral
In mathematics, the Skorokhod integral, often denoted , is an operator of great importance in the theory of stochastic processes. It is named after the Ukrainian mathematician Anatoliy Skorokhod. Part
Paley–Wiener integral
In mathematics, the Paley–Wiener integral is a simple stochastic integral. When applied to classical Wiener space, it is less general than the Itō integral, but the two agree when they are both define
Riemann–Stieltjes integral
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition of this integral was first publish
Pfeffer integral
In mathematics, the Pfeffer integral is an integration technique created by Washek Pfeffer as an attempt to extend the Henstock–Kurzweil integral to a multidimensional domain. This was to be done in s