| dbo:abstract |
In the branch of mathematics known as additive combinatorics, Kneser's theorem can refer to one of several related theorems regarding the sizes of certain sumsets in abelian groups. These are named after Martin Kneser, who published them in 1953 and 1956. They may be regarded as extensions of the Cauchy–Davenport theorem, which also concerns sumsets in groups but is restricted to groups whose order is a prime number. The first three statements deal with sumsets whose size (in various senses) is strictly smaller than the sum of the size of the summands. The last statement deals with the case of equality for Haar measure in connected compact abelian groups. (en) En combinatoire additive, le théorème de Kneser, nommé d'après Martin Kneser, est un énoncé sur les sommes d'ensembles dans les groupes abéliens. (fr) におけるクネーザーの定理（Kneser's theorem）は群の部分集合の加法的性質に関する定理で、整数列のシュニレルマン密度に関するマンの定理（シュニレルマン密度の記事を参照）に対応する定理である。マルティン・クネーザーによって（整数列の下極限密度に関する定理と共に）1953年から1956年にかけて証明され、Kempermanによって下のわかりやすい形にまとめられた。 (ja) |
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dbr:Inequality |
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| rdfs:comment |
En combinatoire additive, le théorème de Kneser, nommé d'après Martin Kneser, est un énoncé sur les sommes d'ensembles dans les groupes abéliens. (fr) におけるクネーザーの定理（Kneser's theorem）は群の部分集合の加法的性質に関する定理で、整数列のシュニレルマン密度に関するマンの定理（シュニレルマン密度の記事を参照）に対応する定理である。マルティン・クネーザーによって（整数列の下極限密度に関する定理と共に）1953年から1956年にかけて証明され、Kempermanによって下のわかりやすい形にまとめられた。 (ja) In the branch of mathematics known as additive combinatorics, Kneser's theorem can refer to one of several related theorems regarding the sizes of certain sumsets in abelian groups. These are named after Martin Kneser, who published them in 1953 and 1956. They may be regarded as extensions of the Cauchy–Davenport theorem, which also concerns sumsets in groups but is restricted to groups whose order is a prime number. (en) |
| rdfs:label |
Satz von Kneser (Abelsche Gruppen) (de) Théorème de Kneser (combinatoire) (fr) Kneser's theorem (combinatorics) (en) クネーザーの定理 (組み合わせ論) (ja) |
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