Denjoy Integral (other)

	Denjoy Integral (other) The Denjoy integral in mathematics can refer to two closely related integrals connected to the work of Arnaud Denjoy: * the ''narrow'' Denjoy integral, or just Denjoy integral, also known as Henstock–Kurzweil integral, * the (more general) ''wide'' Denjoy integral, or Khinchin integral. {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Arnaud Denjoy Arnaud Denjoy (; 5 January 1884 – 21 January 1974) was a French mathematician. Biography Denjoy was born in Auch, Gers. His contributions include work in harmonic analysis and differential equations. His integral was the first to be able to integrate all derivatives. Among his students is Gustave Choquet. He is also known for the more general broad Denjoy integral, or Khinchin integral. Denjoy was an Invited Speaker of the ICM with talk ''Sur une classe d'ensembles parfaits en relation avec les fonctions admettant une dérivée seconde généralisée'' in 1920 at Strasbourg and with talk ''Les equations differentielles periodiques'' in 1950 at Cambridge, Massachusetts. In 1931 he was the president of the Société Mathématique de France. In 1942 he was elected a member of the Académie des sciences and was its president in 1962. Denjoy married in 1923 and was the father of three sons. He died in Paris in 1974. He was an atheist with a strong interest in philosophy, psycho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Henstock–Kurzweil Integral In mathematics, the Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced ), Luzin integral or Perron integral, but not to be confused with the more general wide Denjoy integral – is one of a number of inequivalent definitions of the integral of a function. It is a generalization of the Riemann integral, and in some situations is more general than the Lebesgue integral. In particular, a function is Lebesgue integrable if and only if the function and its absolute value are Henstock–Kurzweil integrable. This integral was first defined by Arnaud Denjoy (1912). Denjoy was interested in a definition that would allow one to integrate functions like :f(x)=\frac\sin\left(\frac\right). This function has a singularity at 0, and is not Lebesgue integrable. However, it seems natural to calculate its integral except over the interval and then let . Trying to create a general theory, Denjoy used t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]