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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 invariant 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".

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rdf:type
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  • Mittelbare Gruppe
  • Amenable group
  • Groupe moyennable
  • Gruppo amenabile
  • 従順群
  • 종순군
  • Аменабельная группа
  • 可均群
rdfs:comment
  • 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。
  • 군론에서, 종순군(從順群, 영어: amenable group)은 군의 작용에 불변인 유한 가법 확률 측도를 정의할 수 있는 국소 콤팩트 위상군이다.
  • 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.
  • 可均群是數學上一個特別的拓撲群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。
  • 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.
  • 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 invariant 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".
  • 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.
  • In matematica, un gruppo amenabile (in inglese amenable group, contrazione di a mean able, cioè di cui si può fare la media) è un gruppo topologico localmente compatto G sui cui è possibile un tipo di operazione media su funzioni limitate che è invariante con la traslazione di elementi del gruppo. Nella , dove G ha una topologia discreta, è utilizzata una definizione più semplice: un gruppo è amenabile se si può dire qual è la percentuale di G che qualsiasi sottoinsieme dato occupa. Se un gruppo ha una , allora è automaticamente amenabile.
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