enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Lebesgue integral - Wikipedia

   en.wikipedia.org/wiki/Lebesgue_integral

   The Lebesgue integral, named after French mathematician Henri Lebesgue, is one way to make this concept rigorous and to extend it to more general functions. The Lebesgue integral is more general than the Riemann integral , which it largely replaced in mathematical analysis since the first half of the 20th century.

3. Lebesgue–Stieltjes integration - Wikipedia

   en.wikipedia.org/wiki/Lebesgue–Stieltjes...

   The Lebesgue–Stieltjes integral ()is defined when : [,] is Borel-measurable and bounded and : [,] is of bounded variation in [a, b] and right-continuous, or when f is non-negative and g is monotone and right-continuous.

4. Absolutely integrable function - Wikipedia

   en.wikipedia.org/wiki/Absolutely_integrable_function

   In Lebesgue integration, this is exactly the requirement for any measurable function f to be considered integrable, with the integral then equaling + (), so that in fact "absolutely integrable" means the same thing as "Lebesgue integrable" for measurable functions.

5. Riemann–Lebesgue lemma - Wikipedia

   en.wikipedia.org/wiki/Riemann–Lebesgue_lemma

   However, the Riemann–Lebesgue lemma does not hold for arbitrary distributions. For example, the Dirac delta function distribution formally has a finite integral over the real line, but its Fourier transform is a constant and does not vanish at infinity.

6. Henri Lebesgue - Wikipedia

   en.wikipedia.org/wiki/Henri_Lebesgue

   Henri Léon Lebesgue ForMemRS [1] (French: [ɑ̃ʁi leɔ̃ ləbɛɡ]; June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an axis and the curve of a function defined for that axis.

7. Dominated convergence theorem - Wikipedia

   en.wikipedia.org/wiki/Dominated_convergence_theorem

   Lebesgue's dominated convergence theorem is a special case of the Fatou–Lebesgue theorem. Below, however, is a direct proof that uses Fatou’s lemma as the essential tool. Since f is the pointwise limit of the sequence (f n) of measurable functions that are dominated by g, it is also measurable and dominated by g, hence it is integrable ...

8. Fatou's lemma - Wikipedia

   en.wikipedia.org/wiki/Fatou's_lemma

   In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after Pierre Fatou. Fatou's lemma can be used to prove the Fatou–Lebesgue theorem and Lebesgue's dominated convergence theorem.

9. Locally integrable function - Wikipedia

   en.wikipedia.org/wiki/Locally_integrable_function

   Measure and integration (as the English translation of the title reads) is a definitive monograph on integration and measure theory: the treatment of the limiting behavior of the integral of various kind of sequences of measure-related structures (measurable functions, measurable sets, measures and their combinations) is somewhat conclusive.