. "Em matem\u00E1tica, especialmente em teoria dos conjuntos, um cardinal n\u00E3o enumer\u00E1vel \u00E9 denominado mensur\u00E1vel se existe uma medida -aditiva, valorada em (ou seja, bivalente) e n\u00E1o trivial sobre o conjunto pot\u00EAncia . Cardinal mensur\u00E1vel \u00E9 considerada uma propriedade de grande cardinal."@pt . . . . . . . . "\u53EF\u6E2C\u57FA\u6578"@zh . . . . . . . . . . . . "Banach"@en . . . "1070898487"^^ . . . . "M\u011B\u0159iteln\u00FD kardin\u00E1l je matematick\u00FD pojem z oblasti teorie mno\u017Ein (kardin\u00E1ln\u00ED aritmetiky). Pat\u0159\u00ED mezi velk\u00E9 kardin\u00E1ly."@cs . . . . . "Cardinal mesurable"@fr . "\uC9D1\uD569\uB860\uC5D0\uC11C \uAC00\uCE21 \uAE30\uC218(\u53EF\u6E2C\u57FA\u6578, \uC601\uC5B4: measurable cardinal)\uB294 \uAE30\uBCF8 \uB9E4\uC7A5\uC73C\uB85C \uC815\uC758\uB420 \uC218 \uC788\uB294 \uAE30\uC218\uC774\uB2E4. \uD070 \uAE30\uC218\uC758 \uD558\uB098\uC774\uB2E4."@ko . . . . . . . "M\u011B\u0159iteln\u00FD kardin\u00E1l je matematick\u00FD pojem z oblasti teorie mno\u017Ein (kardin\u00E1ln\u00ED aritmetiky). Pat\u0159\u00ED mezi velk\u00E9 kardin\u00E1ly."@cs . . . . . "Stefan"@en . . . "1930"^^ . . . . "M\u011B\u0159iteln\u00FD kardin\u00E1l"@cs . . . . "\uAC00\uCE21 \uAE30\uC218"@ko . "Liczba mierzalna \u2013 nieprzeliczalna liczba kardynalna na kt\u00F3rej istnieje -zupe\u0142ny nieg\u0142\u00F3wny ultrafiltr. Liczba rzeczywi\u015Bcie mierzalna to nieprzeliczalna liczba kardynalna na kt\u00F3rej istnieje -addytywna miara, kt\u00F3ra znika na punktach i kt\u00F3ra mierzy wszystkie podzbiory Liczby mierzalne s\u0105 punktem wyj\u015Bciowym dla cz\u0119\u015Bci hierarchii du\u017Cych liczb kardynalnych zwi\u0105zanej z zanurzeniami elementarnymi V w model wewn\u0119trzny M."@pl . "\u6578\u5B78\u4E0A\uFF0C\u53EF\u6E2C\u57FA\u6578\u662F\u4E00\u985E\u5927\u57FA\u6578\u3002\u70BA\u4E86\u5B9A\u7FA9\u6B64\u6982\u5FF5\uFF0C\u8003\u616E\u57FA\u6578 \u03BA \u4E0A\u50C5\u53D6\u5169\u503C\uFF080 \u6216 1\uFF09\u7684\u6E2C\u5EA6\u3002\u5982\u6B64\u7684\u6E2C\u5EA6\u53EF\u770B\u6210\u5C07 \u03BA \u7684\u6240\u6709\u5B50\u96C6\u5206\u6210\u5169\u985E\uFF1A\u5927\u548C\u5C0F\uFF0C\u4F7F\u5F97 \u03BA \u672C\u8EAB\u70BA\u5927\uFF0C\u4F46 \u2205 \u548C\u6240\u6709\u55AE\u5143\u7D20\u96C6\u5408 \u7686\u70BA\u5C0F\uFF0C\u4E14\u5C0F\u96C6\u7684\u88DC\u96C6\u70BA\u5927\uFF0C\u53CD\u4E4B\u4EA6\u7136\u3002\u540C\u6642\u9084\u8981\u6C42\u5C11\u65BC \u03BA \u500B\u5927\u96C6\u7684\u4EA4\u96C6\u4ECD\u70BA\u5927\u3002 \u5177\u6709\u4EE5\u4E0A\u4E8C\u503C\u6E2C\u5EA6\u7684\u4E0D\u53EF\u6578\u57FA\u6578\u662F\u5927\u57FA\u6578\uFF0CZFC \u7121\u6CD5\u8B49\u660E\u5176\u5B58\u5728\u3002 \u53EF\u6E2C\u57FA\u6578\u7684\u6982\u5FF5\u6700\u65E9\u7531\u65AF\u5854\u5C3C\u65AF\u62C9\u592B\u00B7\u70CF\u62C9\u59C6\u65BC 1930 \u5E74\u63D0\u51FA\u3002"@zh . . . "Liczba mierzalna \u2013 nieprzeliczalna liczba kardynalna na kt\u00F3rej istnieje -zupe\u0142ny nieg\u0142\u00F3wny ultrafiltr. Liczba rzeczywi\u015Bcie mierzalna to nieprzeliczalna liczba kardynalna na kt\u00F3rej istnieje -addytywna miara, kt\u00F3ra znika na punktach i kt\u00F3ra mierzy wszystkie podzbiory Liczby mierzalne s\u0105 punktem wyj\u015Bciowym dla cz\u0119\u015Bci hierarchii du\u017Cych liczb kardynalnych zwi\u0105zanej z zanurzeniami elementarnymi V w model wewn\u0119trzny M."@pl . . "Liczba mierzalna"@pl . . . "Stanislaw Ulam"@en . . . "Cardinal mensur\u00E1vel"@pt . . . "Em matem\u00E1tica, especialmente em teoria dos conjuntos, um cardinal n\u00E3o enumer\u00E1vel \u00E9 denominado mensur\u00E1vel se existe uma medida -aditiva, valorada em (ou seja, bivalente) e n\u00E1o trivial sobre o conjunto pot\u00EAncia . Cardinal mensur\u00E1vel \u00E9 considerada uma propriedade de grande cardinal."@pt . . . . . . . "Ulam"@en . "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 \u03BA, or more generally on any set. For a cardinal \u03BA, it can be described as a subdivision of all of its subsets into large and small sets such that \u03BA itself is large, \u2205 and all singletons {\u03B1}, \u03B1 \u2208 \u03BA are small, complements of small sets are large and vice versa. The intersection of fewer than \u03BA large sets is again large. The concept of a measurable cardinal was introduced by Stanislaw Ulam in 1930."@en . "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 \u03BA, or more generally on any set. For a cardinal \u03BA, it can be described as a subdivision of all of its subsets into large and small sets such that \u03BA itself is large, \u2205 and all singletons {\u03B1}, \u03B1 \u2208 \u03BA are small, complements of small sets are large and vice versa. The intersection of fewer than \u03BA 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."@en . . . . . . . . . . . . . . "\u6578\u5B78\u4E0A\uFF0C\u53EF\u6E2C\u57FA\u6578\u662F\u4E00\u985E\u5927\u57FA\u6578\u3002\u70BA\u4E86\u5B9A\u7FA9\u6B64\u6982\u5FF5\uFF0C\u8003\u616E\u57FA\u6578 \u03BA \u4E0A\u50C5\u53D6\u5169\u503C\uFF080 \u6216 1\uFF09\u7684\u6E2C\u5EA6\u3002\u5982\u6B64\u7684\u6E2C\u5EA6\u53EF\u770B\u6210\u5C07 \u03BA \u7684\u6240\u6709\u5B50\u96C6\u5206\u6210\u5169\u985E\uFF1A\u5927\u548C\u5C0F\uFF0C\u4F7F\u5F97 \u03BA \u672C\u8EAB\u70BA\u5927\uFF0C\u4F46 \u2205 \u548C\u6240\u6709\u55AE\u5143\u7D20\u96C6\u5408 \u7686\u70BA\u5C0F\uFF0C\u4E14\u5C0F\u96C6\u7684\u88DC\u96C6\u70BA\u5927\uFF0C\u53CD\u4E4B\u4EA6\u7136\u3002\u540C\u6642\u9084\u8981\u6C42\u5C11\u65BC \u03BA \u500B\u5927\u96C6\u7684\u4EA4\u96C6\u4ECD\u70BA\u5927\u3002 \u5177\u6709\u4EE5\u4E0A\u4E8C\u503C\u6E2C\u5EA6\u7684\u4E0D\u53EF\u6578\u57FA\u6578\u662F\u5927\u57FA\u6578\uFF0CZFC \u7121\u6CD5\u8B49\u660E\u5176\u5B58\u5728\u3002 \u53EF\u6E2C\u57FA\u6578\u7684\u6982\u5FF5\u6700\u65E9\u7531\u65AF\u5854\u5C3C\u65AF\u62C9\u592B\u00B7\u70CF\u62C9\u59C6\u65BC 1930 \u5E74\u63D0\u51FA\u3002"@zh . . . . . "248102"^^ . . . "Stefan Banach"@en . . . . "14409"^^ . . . "\uC9D1\uD569\uB860\uC5D0\uC11C \uAC00\uCE21 \uAE30\uC218(\u53EF\u6E2C\u57FA\u6578, \uC601\uC5B4: measurable cardinal)\uB294 \uAE30\uBCF8 \uB9E4\uC7A5\uC73C\uB85C \uC815\uC758\uB420 \uC218 \uC788\uB294 \uAE30\uC218\uC774\uB2E4. \uD070 \uAE30\uC218\uC758 \uD558\uB098\uC774\uB2E4."@ko . . . "Measurable cardinal"@en . "Stanislaw"@en . . . . . . . . . "En math\u00E9matiques, un cardinal mesurable est un cardinal sur lequel existe une mesure d\u00E9finie pour tout sous-ensemble. Cette propri\u00E9t\u00E9 fait qu'un tel cardinal est un grand cardinal."@fr . . . . . . "En math\u00E9matiques, un cardinal mesurable est un cardinal sur lequel existe une mesure d\u00E9finie pour tout sous-ensemble. Cette propri\u00E9t\u00E9 fait qu'un tel cardinal est un grand cardinal."@fr . . . .