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.


  • 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) [1994], "Hellinger integral", in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
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