. . . . "Darboux's theorem (analysis)"@en . "Il teorema di Darboux \u00E8 un teorema dell'analisi matematica che prende il nome da Jean Gaston Darboux. Esso afferma che tutte le funzioni che risultano dalla derivazione di altre funzioni presentano la propriet\u00E0 del valore intermedio: l'immagine di un intervallo \u00E8 ancora un intervallo. \u00C8 da notare che quando \u00E8 differenziabile con derivata continua (cio\u00E8 ) questo \u00E8 implicitamente vero per il teorema dei valori intermedi, ma anche quando non \u00E8 continua il teorema di Darboux pone forti limiti alle sue variazioni."@it . . . . . "Darboux's theorem"@en . . "In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation of another function has the intermediate value property: the image of an interval is also an interval. When \u0192 is continuously differentiable (\u0192 in C1([a,b])), this is a consequence of the intermediate value theorem. But even when \u0192\u2032 is not continuous, Darboux's theorem places a severe restriction on what it can be."@en . . . . . "En math\u00E9matiques, et plus particuli\u00E8rement en analyse, le th\u00E9or\u00E8me de Darboux est un th\u00E9or\u00E8me d\u00E9montr\u00E9 par Gaston Darboux en 1875 et qui \u00E9tend le th\u00E9or\u00E8me des valeurs interm\u00E9diaires aux fonctions non n\u00E9cessairement continues mais seulement d\u00E9riv\u00E9es de fonctions r\u00E9elles."@fr . . . "4130888"^^ . . . . "In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation of another function has the intermediate value property: the image of an interval is also an interval. When \u0192 is continuously differentiable (\u0192 in C1([a,b])), this is a consequence of the intermediate value theorem. But even when \u0192\u2032 is not continuous, Darboux's theorem places a severe restriction on what it can be."@en . . "\u0422\u0435\u043E\u0440\u0435\u0301\u043C\u0430 \u043E \u0441\u0432\u043E\u0301\u0439\u0441\u0442\u0432\u0435 \u0414\u0430\u0440\u0431\u0443\u0301 (\u0414-\u0441\u0432\u043E\u0301\u0439\u0441\u0442\u0432\u0435) \u0434\u043B\u044F \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0301\u0432\u043D\u043E\u0439 \u0444\u0443\u0301\u043D\u043A\u0446\u0438\u0438 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u043C \u0430\u043D\u0430\u043B\u0438\u0437\u0435 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442, \u0447\u0442\u043E \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u044B\u0439 \u043E\u0431\u0440\u0430\u0437 \u043E\u0442\u0440\u0435\u0437\u043A\u0430 \u0435\u0441\u0442\u044C \u043E\u0442\u0440\u0435\u0437\u043E\u043A."@ru . . "Teorema di Darboux"@it . . . . "Teorema de Darboux"@pt . . . "6967"^^ . . "Th\u00E9or\u00E8me de Darboux (analyse)"@fr . "Darboux theorem"@en . . . . . . "p/d030190"@en . "Em an\u00E1lise real, o teorema de Darboux, cujo nome se refere ao matem\u00E1tico franc\u00EAs Gaston Darboux, afirma que as derivadas de fun\u00E7\u00F5es deriv\u00E1veis satisfazem a propriedade dos valores interm\u00E9dios: a imagem de um intervalo \u00E9 novamente um intervalo."@pt . . "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u0414\u0430\u0440\u0431\u0443 \u2014 \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u0430\u043D\u0430\u043B\u0456\u0437\u0456, \u0449\u043E \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454 \u2014 \u044F\u043A\u0449\u043E \u0434\u0435\u044F\u043A\u0430 \u0444\u0443\u043D\u043A\u0446\u0456\u044F \u043D\u0430 \u0437\u0430\u043C\u043A\u043D\u0443\u0442\u043E\u043C\u0443 \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0443 \u0454 \u043F\u043E\u0445\u0456\u0434\u043D\u043E\u044E \u0456\u043D\u0448\u043E\u0457 \u0444\u0443\u043D\u043A\u0446\u0456\u0457, \u0442\u043E \u043D\u0430 \u0446\u044C\u043E\u043C\u0443 \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0443 \u0432\u043E\u043D\u0430 \u043D\u0430\u0431\u0443\u0432\u0430\u0454 \u0443\u0441\u0456\u0445 \u043F\u0440\u043E\u043C\u0456\u0436\u043D\u0438\u0445 \u0437\u043D\u0430\u0447\u0435\u043D\u044C \u043C\u0456\u0436 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F\u043C\u0438 \u043D\u0430 \u043A\u0440\u0430\u044F\u0445 \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0430. \u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0416\u0430\u043D\u0430 \u0413\u0430\u0441\u0442\u043E\u043D\u0430 \u0414\u0430\u0440\u0431\u0443. \u0423 \u0432\u0438\u043F\u0430\u0434\u043A\u0443, \u044F\u043A\u0449\u043E \u043F\u043E\u0445\u0456\u0434\u043D\u0430 \u0454 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u043E\u044E, \u0434\u0430\u043D\u0435 \u0442\u0432\u0435\u0440\u0434\u0436\u0435\u043D\u043D\u044F \u0454 \u043D\u0430\u0441\u043B\u0456\u0434\u043A\u043E\u043C \u0442\u0435\u043E\u0440\u0435\u043C\u0438 \u0411\u043E\u043B\u044C\u0446\u0430\u043D\u043E-\u041A\u043E\u0448\u0456. \u041F\u0440\u043E\u0442\u0435 \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0414\u0430\u0440\u0431\u0443 \u0441\u043F\u0440\u0430\u0432\u0435\u0434\u043B\u0438\u0432\u0430 \u043D\u0430\u0432\u0456\u0442\u044C \u044F\u043A\u0449\u043E \u043F\u043E\u0445\u0456\u0434\u043D\u0430 \u043D\u0435 \u0454 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u043E\u044E."@uk . . . . . . "\u5728\u5B9E\u5206\u6790\u4E2D\uFF0C\u8FBE\u5E03\u5B9A\u7406\uFF08\u82F1\u8A9E\uFF1ADarboux's theorem\uFF09\u5F97\u540D\u4E8E\u8BA9\u00B7\u52A0\u65AF\u4E1C\u00B7\u8FBE\u5E03\u3002\u8FBE\u5E03\u5B9A\u7406\u8BF4\u660E\u6240\u6709\u7684\u5B9E\u5BFC\u51FD\u6570\uFF08\u662F\u67D0\u4E2A\u5B9E\u503C\u51FD\u6570\u7684\u5BFC\u6570\u7684\u51FD\u6570\uFF09\u90FD\u5177\u6709\u4ECB\u503C\u6027\u8D28\uFF1A\u4EFB\u4E00\u4E2A\u533A\u95F4\u5173\u4E8E\u5B9E\u5BFC\u51FD\u6570\u7684\u503C\u57DF\u4ECD\u662F\u533A\u95F4\u3002\u5373\u662F\u8BF4\uFF0C\u82E5 f \u4E3A\u53EF\u5BFC\u51FD\u6570\uFF0C\u5219\u5BF9\u4EFB\u610F\u533A\u95F4I\uFF0Cf\u2032(I) \u4ECD\u4E3A\u533A\u95F4\u3002 \u5F53\u51FD\u6570 f \u662F\u4E00\u9636\u8FDE\u7EED\u53EF\u5BFC\u51FD\u6570\uFF08C1\uFF09\u65F6\uFF0C\u7531\u4ECB\u503C\u5B9A\u7406\uFF0C\u8FBE\u5E03\u5B9A\u7406\u663E\u7136\u6210\u7ACB\u3002\u5F53\u5BFC\u51FD\u6570 f\u2032 \u4E0D\u8FDE\u7EED\u65F6\uFF0C\u8FBE\u5E03\u5B9A\u7406\u8BF4\u660E f\u2032 \u4ECD\u5177\u6709\u4ECB\u503C\u6027\u8D28\u3002"@zh . "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u0414\u0430\u0440\u0431\u0443 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u0430\u043D\u0430\u043B\u0456\u0437\u0456"@uk . "Em an\u00E1lise real, o teorema de Darboux, cujo nome se refere ao matem\u00E1tico franc\u00EAs Gaston Darboux, afirma que as derivadas de fun\u00E7\u00F5es deriv\u00E1veis satisfazem a propriedade dos valores interm\u00E9dios: a imagem de um intervalo \u00E9 novamente um intervalo."@pt . . . "\uBBF8\uC801\uBD84\uD559\uACFC \uC704\uC0C1\uC218\uD559\uC5D0\uC11C \uB2E4\uB974\uBD80 \uD568\uC218(\uC601\uC5B4: Darboux\u2019s function)\uB294 \uC5F0\uACB0 \uC9D1\uD569\uC758 \uC0C1\uC774 \uC5F0\uACB0 \uC9D1\uD569\uC778 \uD568\uC218\uC774\uB2E4. \uC2E4\uC218\uC5D0\uC11C \uC2E4\uC218\uB85C \uAC00\uB294 \uD568\uC218\uC758 \uACBD\uC6B0 \uC774\uB294 \uAD6C\uAC04\uC758 \uC0C1\uC774 \uAD6C\uAC04\uC778 \uD568\uC218\uC640 \uB3D9\uCE58\uC774\uB2E4. \uB2E4\uB974\uBD80 \uC815\uB9AC(\uC601\uC5B4: Darboux\u2019s theorem) \uB610\uB294 \uB2E4\uB974\uBD80 \uC911\uAC04\uAC12 \uC815\uB9AC(\uC601\uC5B4: Darboux\u2019s intermediate value theorem)\uC5D0 \uB530\uB974\uBA74, \uC2E4\uC218 \uAD6C\uAC04\uC5D0\uC11C \uC2E4\uC218\uB85C \uAC00\uB294 \uBBF8\uBD84 \uAC00\uB2A5 \uD568\uC218\uC758 \uB3C4\uD568\uC218\uB294 \uD56D\uC0C1 \uB2E4\uB974\uBD80 \uD568\uC218\uC774\uB2E4. \uC774\uB294 \uC911\uAC04\uAC12 \uC815\uB9AC\uC758 \uD55C \uAC00\uC9C0 \uC77C\uBC18\uD654\uC774\uB2E4."@ko . . . . . "\u8FBE\u5E03\u5B9A\u7406"@zh . . "\uB2E4\uB974\uBD80 \uD568\uC218"@ko . . . "En math\u00E9matiques, et plus particuli\u00E8rement en analyse, le th\u00E9or\u00E8me de Darboux est un th\u00E9or\u00E8me d\u00E9montr\u00E9 par Gaston Darboux en 1875 et qui \u00E9tend le th\u00E9or\u00E8me des valeurs interm\u00E9diaires aux fonctions non n\u00E9cessairement continues mais seulement d\u00E9riv\u00E9es de fonctions r\u00E9elles."@fr . . "\uBBF8\uC801\uBD84\uD559\uACFC \uC704\uC0C1\uC218\uD559\uC5D0\uC11C \uB2E4\uB974\uBD80 \uD568\uC218(\uC601\uC5B4: Darboux\u2019s function)\uB294 \uC5F0\uACB0 \uC9D1\uD569\uC758 \uC0C1\uC774 \uC5F0\uACB0 \uC9D1\uD569\uC778 \uD568\uC218\uC774\uB2E4. \uC2E4\uC218\uC5D0\uC11C \uC2E4\uC218\uB85C \uAC00\uB294 \uD568\uC218\uC758 \uACBD\uC6B0 \uC774\uB294 \uAD6C\uAC04\uC758 \uC0C1\uC774 \uAD6C\uAC04\uC778 \uD568\uC218\uC640 \uB3D9\uCE58\uC774\uB2E4. \uB2E4\uB974\uBD80 \uC815\uB9AC(\uC601\uC5B4: Darboux\u2019s theorem) \uB610\uB294 \uB2E4\uB974\uBD80 \uC911\uAC04\uAC12 \uC815\uB9AC(\uC601\uC5B4: Darboux\u2019s intermediate value theorem)\uC5D0 \uB530\uB974\uBA74, \uC2E4\uC218 \uAD6C\uAC04\uC5D0\uC11C \uC2E4\uC218\uB85C \uAC00\uB294 \uBBF8\uBD84 \uAC00\uB2A5 \uD568\uC218\uC758 \uB3C4\uD568\uC218\uB294 \uD56D\uC0C1 \uB2E4\uB974\uBD80 \uD568\uC218\uC774\uB2E4. \uC774\uB294 \uC911\uAC04\uAC12 \uC815\uB9AC\uC758 \uD55C \uAC00\uC9C0 \uC77C\uBC18\uD654\uC774\uB2E4."@ko . . . "3055"^^ . . . "Darbouxova v\u011Bta"@cs . . "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u0414\u0430\u0440\u0431\u0443 \u2014 \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u043E\u043C\u0443 \u0430\u043D\u0430\u043B\u0456\u0437\u0456, \u0449\u043E \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454 \u2014 \u044F\u043A\u0449\u043E \u0434\u0435\u044F\u043A\u0430 \u0444\u0443\u043D\u043A\u0446\u0456\u044F \u043D\u0430 \u0437\u0430\u043C\u043A\u043D\u0443\u0442\u043E\u043C\u0443 \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0443 \u0454 \u043F\u043E\u0445\u0456\u0434\u043D\u043E\u044E \u0456\u043D\u0448\u043E\u0457 \u0444\u0443\u043D\u043A\u0446\u0456\u0457, \u0442\u043E \u043D\u0430 \u0446\u044C\u043E\u043C\u0443 \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0443 \u0432\u043E\u043D\u0430 \u043D\u0430\u0431\u0443\u0432\u0430\u0454 \u0443\u0441\u0456\u0445 \u043F\u0440\u043E\u043C\u0456\u0436\u043D\u0438\u0445 \u0437\u043D\u0430\u0447\u0435\u043D\u044C \u043C\u0456\u0436 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F\u043C\u0438 \u043D\u0430 \u043A\u0440\u0430\u044F\u0445 \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0430. \u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u044C\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u0416\u0430\u043D\u0430 \u0413\u0430\u0441\u0442\u043E\u043D\u0430 \u0414\u0430\u0440\u0431\u0443. \u0423 \u0432\u0438\u043F\u0430\u0434\u043A\u0443, \u044F\u043A\u0449\u043E \u043F\u043E\u0445\u0456\u0434\u043D\u0430 \u0454 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u043E\u044E, \u0434\u0430\u043D\u0435 \u0442\u0432\u0435\u0440\u0434\u0436\u0435\u043D\u043D\u044F \u0454 \u043D\u0430\u0441\u043B\u0456\u0434\u043A\u043E\u043C \u0442\u0435\u043E\u0440\u0435\u043C\u0438 \u0411\u043E\u043B\u044C\u0446\u0430\u043D\u043E-\u041A\u043E\u0448\u0456. \u041F\u0440\u043E\u0442\u0435 \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0414\u0430\u0440\u0431\u0443 \u0441\u043F\u0440\u0430\u0432\u0435\u0434\u043B\u0438\u0432\u0430 \u043D\u0430\u0432\u0456\u0442\u044C \u044F\u043A\u0449\u043E \u043F\u043E\u0445\u0456\u0434\u043D\u0430 \u043D\u0435 \u0454 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u043E\u044E."@uk . . . "1083848703"^^ . . "Il teorema di Darboux \u00E8 un teorema dell'analisi matematica che prende il nome da Jean Gaston Darboux. Esso afferma che tutte le funzioni che risultano dalla derivazione di altre funzioni presentano la propriet\u00E0 del valore intermedio: l'immagine di un intervallo \u00E8 ancora un intervallo. \u00C8 da notare che quando \u00E8 differenziabile con derivata continua (cio\u00E8 ) questo \u00E8 implicitamente vero per il teorema dei valori intermedi, ma anche quando non \u00E8 continua il teorema di Darboux pone forti limiti alle sue variazioni."@it . "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u043E \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0435 \u0414\u0430\u0440\u0431\u0443 \u0434\u043B\u044F \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u043E\u0439 \u0444\u0443\u043D\u043A\u0446\u0438\u0438"@ru . . . . . . . . . . "\u5728\u5B9E\u5206\u6790\u4E2D\uFF0C\u8FBE\u5E03\u5B9A\u7406\uFF08\u82F1\u8A9E\uFF1ADarboux's theorem\uFF09\u5F97\u540D\u4E8E\u8BA9\u00B7\u52A0\u65AF\u4E1C\u00B7\u8FBE\u5E03\u3002\u8FBE\u5E03\u5B9A\u7406\u8BF4\u660E\u6240\u6709\u7684\u5B9E\u5BFC\u51FD\u6570\uFF08\u662F\u67D0\u4E2A\u5B9E\u503C\u51FD\u6570\u7684\u5BFC\u6570\u7684\u51FD\u6570\uFF09\u90FD\u5177\u6709\u4ECB\u503C\u6027\u8D28\uFF1A\u4EFB\u4E00\u4E2A\u533A\u95F4\u5173\u4E8E\u5B9E\u5BFC\u51FD\u6570\u7684\u503C\u57DF\u4ECD\u662F\u533A\u95F4\u3002\u5373\u662F\u8BF4\uFF0C\u82E5 f \u4E3A\u53EF\u5BFC\u51FD\u6570\uFF0C\u5219\u5BF9\u4EFB\u610F\u533A\u95F4I\uFF0Cf\u2032(I) \u4ECD\u4E3A\u533A\u95F4\u3002 \u5F53\u51FD\u6570 f \u662F\u4E00\u9636\u8FDE\u7EED\u53EF\u5BFC\u51FD\u6570\uFF08C1\uFF09\u65F6\uFF0C\u7531\u4ECB\u503C\u5B9A\u7406\uFF0C\u8FBE\u5E03\u5B9A\u7406\u663E\u7136\u6210\u7ACB\u3002\u5F53\u5BFC\u51FD\u6570 f\u2032 \u4E0D\u8FDE\u7EED\u65F6\uFF0C\u8FBE\u5E03\u5B9A\u7406\u8BF4\u660E f\u2032 \u4ECD\u5177\u6709\u4ECB\u503C\u6027\u8D28\u3002"@zh . . . "\u0422\u0435\u043E\u0440\u0435\u0301\u043C\u0430 \u043E \u0441\u0432\u043E\u0301\u0439\u0441\u0442\u0432\u0435 \u0414\u0430\u0440\u0431\u0443\u0301 (\u0414-\u0441\u0432\u043E\u0301\u0439\u0441\u0442\u0432\u0435) \u0434\u043B\u044F \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0301\u0432\u043D\u043E\u0439 \u0444\u0443\u0301\u043D\u043A\u0446\u0438\u0438 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u043C \u0430\u043D\u0430\u043B\u0438\u0437\u0435 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442, \u0447\u0442\u043E \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u044B\u0439 \u043E\u0431\u0440\u0430\u0437 \u043E\u0442\u0440\u0435\u0437\u043A\u0430 \u0435\u0441\u0442\u044C \u043E\u0442\u0440\u0435\u0437\u043E\u043A."@ru .