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In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun on "mean". If a group has a Følner sequence then it is automatically amenable.

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rdf:type	yago:WikicatTopologicalGroups yago:Abstraction100002137 yago:Group100031264
rdfs:label	Amenable group (en) Mittelbare Gruppe (de) Groupe moyennable (fr) Gruppo amenabile (it) 종순군 (ko) 従順群 (ja) Аменабельная группа (ru) 可均群 (zh)
rdfs:comment	군론에서 종순군(從順群, 영어: amenable group)은 군의 작용에 불변인 유한 가법 확률 측도를 정의할 수 있는 국소 콤팩트 위상군이다. (ko) 従順群（じゅうじゅんぐん、英語: amenable group）は、局所コンパクト群の一種。 (ja) Аменабельная группа — локально компактная топологическая группа G, в которой возможно ввести операцию усреднения на ограниченных функциях на этой группе, инвариантную относительно умножения на любой элемент группы. (ru) 可均群是數學上一個特別的局部緊拓撲群G，具備了一種為在G上的有界函數取平均的操作，而且G在函數上的群作用，不會改變所取得的平均。 (zh) In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun on "mean". If a group has a Følner sequence then it is automatically amenable. (en) Mittelbare Gruppe ist ein Begriff aus dem mathematischen Teilgebiet der harmonischen Analyse. Es handelt sich dabei um lokalkompakte Gruppen, auf denen eine gewisse Mittelungsfunktion, ein sogenanntes Mittel, existiert. (de) En mathématiques, un groupe moyennable (parfois appelé groupe amenable par calque de l'anglais) est un groupe topologique localement compact qu'on peut munir d'une opération de « moyenne » sur les fonctions bornées, invariante par les translations par les éléments du groupe. La définition initiale, donnée à partir d'une mesure (simplement additive) des sous-ensembles du groupe, fut proposée par John von Neumann en 1929 à la suite de son analyse du paradoxe de Banach-Tarski. (fr) In matematica, un gruppo amenabile (in inglese amenable group, dal significato di trattabile, assoggettabile, riducibile) è un gruppo topologico localmente compatto G su cui è possibile un tipo di operazione media su funzioni limitate che è invariante con la traslazione di elementi del gruppo. La proprietà amenabilità ha un gran numero di formulazioni equivalenti. Nel campo della analisi, la definizione è in termini di funzionali lineari. Un modo intuitivo per comprendere questa versione è che il supporto della rappresentazione regolare sia lo spazio intero della rappresentazione irriducibile. (it)
dcterms:subject	Geometric group theory Topological groups
Wikipage page ID	657430 (xsd:integer)
Wikipage revision ID	1110985749 (xsd:integer)
Link from a Wikipage to another Wikipage	Amenable Banach algebra Elementary amenable group Nicolas Monod Bounded function Almost everywhere Annals of Mathematics John von Neumann Index of a subgroup Invariant (mathematics) Von Neumann algebra Uniformly bounded representation Periodic group Geometric group theory Compact space Convex set Convolution Mathematical analysis Mathematics Measure (mathematics) Nuclear C-algebra Simple group Second-countable space Fundamental theorem of finitely generated abelian groups German language Ornstein isomorphism theorem Linear functionals Locally compact Locally convex topological vector space Commentarii Mathematici Helvetici Fundamenta Mathematicae Fundamental group Journal d'Analyse Mathématique Spectral theory Markov–Kakutani fixed-point theorem Banach space Banach–Tarski paradox Topological groups Topological group Følner sequence Haar measure Hausdorff space Irreducible representation Linear group Affine transformation Algebraic geometry Discrete group Kazhdan's property (T) Simplicial complex Regular representation Group (mathematics) Hahn–Banach theorem Jacques Tits Counting measure Terry Tao Abelian group L2-space Lebesgue integration Support (mathematics) Discrete topology Tits alternative Topology (journal) Direct product of groups Axiom of choice Borel regular measure Bulletin of the AMS C-algebra Free group Grigorchuk group Group algebra of a locally compact group Group extension Growth rate (group theory) Integer Sequence space Solvable group Von Neumann conjecture FC-group Finite group

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