Hellinger integral

In mathematics, the Hellinger integral is an integral introduced by Hellinger (1909) that is a special case of the Kolmogorov integral. It is used to define the Hellinger distance in probability theory.

References

Hellinger, E. (1909), "Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen", Journal für die reine und angewandte Mathematik (in German), 136: 210–271, doi:10.1515/crll.1909.136.210, JFM 40.0393.01
Hobson, E. W. (1958), The theory of functions of a real variable and the theory of Fourier's series. Vol. I, New York: Dover Publications, pp. XV+736, MR 0092828, Zbl 0081.27702
Vinogradova, I. A. (2001), "Hellinger integral", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

Integrals

Numerical integration	Riemann integral Lebesgue integral Burkill integral Bochner integral Daniell integral Darboux integral Henstock–Kurzweil integral Haar integral Hellinger integral Khinchin integral Kolmogorov integral Lebesgue–Stieltjes integral Pettis integral Pfeffer integral Riemann–Stieltjes integral Regulated integral

Methods	Integration by parts Integration by substitution Inverse function integration Order of integration (calculus) trigonometric substitution Integration by partial fractions Integration by reduction formulae Integration using parametric derivatives Integration using Euler's formula Differentiation under the integral sign Contour integration

Improper Integrals	Improper integral Gaussian integral

Stochastic integrals	Itō integral Stratonovich integral Skorokhod integral

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