Definitions of mathematical integration

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. One of the main difficulties with the traditional formulation of the Lebesgue integral is that it requires the initial development of a workable measure theory before any useful results for the integral can be obtained. However, an alternative approach is available, developed by Percy J. Daniell that does not suffer from this deficiency, and has a few significant advantages over the traditional formulation, especially as the integral is generalized into higher-dimensional spaces and further generalizations such as the Stieltjes integral. The basic idea involves the axiomatization of the integral. (Wikipedia).

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Related pages

Bochner integral | Bounded variation | Lebesgue measure | Absolute value | Functional analysis | Fubini's theorem | Indicator function | Step function | Almost everywhere | Continuous function | Riesz–Fischer theorem | Fatou's lemma | Banach space | Mathematics | Null set | Riemann integral | Lebesgue–Stieltjes integration | Riemann–Stieltjes integral | Radon–Nikodym theorem