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In mathematics, '''Kneser's theorem''' is an [[Inequality (mathematics)|inequality]] among the sizes of certain [[sumset]]s in [[abelian group]]s. It belongs to the field of [[additive combinatorics]], and is named after [[Martin Kneser]], who published it in 1953.<ref>{{cite journal | first=Martin | last=Kneser | title=Abschätzungen der asymptotischen Dichte von Summenmengen | language=German | journal=[[Math. Zeitschr.]] | volume=58 | year=1953 | pages=459–484 | zbl=0051.28104 }}
</ref> It may be regarded as an extension of the [[Cauchy–Davenport theorem]], which also concerns sumsets in groups but is restricted to groups whose [[Order (group theory)|order]] is a [[prime number]].<ref name=GR143>{{harvtxt|Geroldinger
==Statement==
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==References==
* {{cite book | editor1-last=Geroldinger | editor1-first=Alfred | editor2-last=Ruzsa | editor2-first=Imre Z. | editor2-link = Imre Z. Ruzsa | others=Elsholtz, C.; Freiman, G.; Hamidoune, Y. O.; Hegyvári, N.; Károlyi, G.; Nathanson, M.; Solymosi, J.; Stanchescu, Y. With a foreword by Javier Cilleruelo, Marc Noy and Oriol Serra (Coordinators of the DocCourse) | title=Combinatorial number theory and additive group theory | series=Advanced Courses in Mathematics CRM Barcelona | ___location=Basel | publisher=Birkhäuser | year=2009 | isbn=978-3-7643-8961-1 | zbl=1177.11005|ref=harv }}
* {{cite book | first=Melvyn B. | last=Nathanson | authorlink = Melvyn B. Nathanson | title=Additive Number Theory: Inverse Problems and the Geometry of Sumsets | volume=165 | series=[[Graduate Texts in Mathematics]] | publisher=[[Springer-Verlag]] | year=1996 | isbn=0-387-94655-1 | zbl=0859.11003 | pages=109–132 }}
* {{citation | first1=Terence | last1=Tao | author1-link=Terence Tao | first2=Van H. | last2=Vu | title=Additive Combinatorics | year=2010 | publisher=[[Cambridge University Press]] | place=[[Cambridge]] | isbn=978-0-521-13656-3 | zbl=1179.11002 }}
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