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Statements

Subject Item
dbr:Measurable_cardinal
rdf:type
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可測基數 Cardinal mesurable Měřitelný kardinál 가측 기수 Liczba mierzalna Cardinal mensurável Measurable cardinal
rdfs:comment
Měřitelný kardinál je matematický pojem z oblasti teorie množin (kardinální aritmetiky). Patří mezi velké kardinály. 집합론에서 가측 기수(可測基數, 영어: measurable cardinal)는 기본 매장으로 정의될 수 있는 기수이다. 큰 기수의 하나이다. 數學上,可測基數是一類大基數。為了定義此概念,考慮基數 κ 上僅取兩值(0 或 1)的測度。如此的測度可看成將 κ 的所有子集分成兩類:大和小,使得 κ 本身為大,但 ∅ 和所有單元素集合 皆為小,且小集的補集為大,反之亦然。同時還要求少於 κ 個大集的交集仍為大。 具有以上二值測度的不可數基數是大基數,ZFC 無法證明其存在。 可測基數的概念最早由斯塔尼斯拉夫·烏拉姆於 1930 年提出。 Liczba mierzalna – nieprzeliczalna liczba kardynalna na której istnieje -zupełny niegłówny ultrafiltr. Liczba rzeczywiście mierzalna to nieprzeliczalna liczba kardynalna na której istnieje -addytywna miara, która znika na punktach i która mierzy wszystkie podzbiory Liczby mierzalne są punktem wyjściowym dla części hierarchii dużych liczb kardynalnych związanej z zanurzeniami elementarnymi V w model wewnętrzny M. Em matemática, especialmente em teoria dos conjuntos, um cardinal não enumerável é denominado mensurável se existe uma medida -aditiva, valorada em (ou seja, bivalente) e náo trivial sobre o conjunto potência . Cardinal mensurável é considerada uma propriedade de grande cardinal. In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more generally on any set. For a cardinal κ, it can be described as a subdivision of all of its subsets into large and small sets such that κ itself is large, ∅ and all singletons {α}, α ∈ κ are small, complements of small sets are large and vice versa. The intersection of fewer than κ large sets is again large. The concept of a measurable cardinal was introduced by Stanislaw Ulam in 1930. En mathématiques, un cardinal mesurable est un cardinal sur lequel existe une mesure définie pour tout sous-ensemble. Cette propriété fait qu'un tel cardinal est un grand cardinal.
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1070898487
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dbpedia-zh:可測基數 wikidata:Q925445 dbpedia-ko:가측_기수 dbpedia-cs:Měřitelný_kardinál dbpedia-fr:Cardinal_mesurable dbpedia-pt:Cardinal_mensurável dbpedia-he:מונה_מדיד dbpedia-pl:Liczba_mierzalna dbpedia-hu:Mérhető_számosság n24:54f8s freebase:m.01kwmm yago-res:Measurable_cardinal
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dbp:authorlink
Stanislaw Ulam Stefan Banach
dbp:first
Stefan Stanislaw
dbp:last
Banach Ulam
dbp:year
1930
dbo:abstract
Em matemática, especialmente em teoria dos conjuntos, um cardinal não enumerável é denominado mensurável se existe uma medida -aditiva, valorada em (ou seja, bivalente) e náo trivial sobre o conjunto potência . Cardinal mensurável é considerada uma propriedade de grande cardinal. Měřitelný kardinál je matematický pojem z oblasti teorie množin (kardinální aritmetiky). Patří mezi velké kardinály. Liczba mierzalna – nieprzeliczalna liczba kardynalna na której istnieje -zupełny niegłówny ultrafiltr. Liczba rzeczywiście mierzalna to nieprzeliczalna liczba kardynalna na której istnieje -addytywna miara, która znika na punktach i która mierzy wszystkie podzbiory Liczby mierzalne są punktem wyjściowym dla części hierarchii dużych liczb kardynalnych związanej z zanurzeniami elementarnymi V w model wewnętrzny M. In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more generally on any set. For a cardinal κ, it can be described as a subdivision of all of its subsets into large and small sets such that κ itself is large, ∅ and all singletons {α}, α ∈ κ are small, complements of small sets are large and vice versa. The intersection of fewer than κ large sets is again large. It turns out that uncountable cardinals endowed with a two-valued measure are large cardinals whose existence cannot be proved from ZFC. The concept of a measurable cardinal was introduced by Stanislaw Ulam in 1930. 數學上,可測基數是一類大基數。為了定義此概念,考慮基數 κ 上僅取兩值(0 或 1)的測度。如此的測度可看成將 κ 的所有子集分成兩類:大和小,使得 κ 本身為大,但 ∅ 和所有單元素集合 皆為小,且小集的補集為大,反之亦然。同時還要求少於 κ 個大集的交集仍為大。 具有以上二值測度的不可數基數是大基數,ZFC 無法證明其存在。 可測基數的概念最早由斯塔尼斯拉夫·烏拉姆於 1930 年提出。 집합론에서 가측 기수(可測基數, 영어: measurable cardinal)는 기본 매장으로 정의될 수 있는 기수이다. 큰 기수의 하나이다. En mathématiques, un cardinal mesurable est un cardinal sur lequel existe une mesure définie pour tout sous-ensemble. Cette propriété fait qu'un tel cardinal est un grand cardinal.
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