Hellinger integral: Difference between revisions
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In mathematics, the '''Hellinger integral''' is an integral introduced by {{harvs|txt|last=Hellinger|year=1909}} that is a special case of the [[Kolmogorov integral]]. |
In mathematics, the '''Hellinger integral''' is an integral introduced by {{harvs|txt|last=Hellinger|authorlink=Ernst Hellinger|year=1909}} that is a special case of the [[Kolmogorov integral]]. It is used to define the [[Hellinger distance]] in probability theory. |
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==References== |
==References== |
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*{{Citation |
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| ⚫ | |||
| last = Hellinger |
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| first = E. |
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| author-link = Ernst Hellinger |
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| title = Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen |
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| url = http://resolver.sub.uni-goettingen.de/purl?GDZPPN002166941 |
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| year = 1909 |
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| journal = [[Journal für die reine und angewandte Mathematik]] |
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| language = German |
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| volume = 136 |
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| pages = 210–271 |
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| jfm = 40.0393.01 |
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| doi=10.1515/crll.1909.136.210 |
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}} |
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*{{Citation |
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| last1 = Hobson |
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| first1 = E. W. |
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| title = The theory of functions of a real variable and the theory of Fourier's series. Vol. I |
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| url=https://books.google.com/books?id=LCc9AAAAIAAJ |
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| publisher = [[Dover Publications]] |
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| location = New York |
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| pages = XV+736 |
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| mr = 0092828 |
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| zbl = 0081.27702 |
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| year = 1958}} |
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| ⚫ | |||
{{integral}} |
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[[Category:Definitions of mathematical integration]] |
[[Category:Definitions of mathematical integration]] |
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Latest revision as of 01:37, 15 November 2015
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
[edit]- 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", Encyclopedia of Mathematics, EMS Press