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In mathematical analysis, Glaeser's continuity theorem is a characterization of the continuity of the derivative of the square roots of functions of class . It was introduced in 1963 by Georges Glaeser, and was later simplified by Jean Dieudonné. The theorem states: Let be a function of class in an open set U contained in , then is of class in U if and only if its partial derivatives of first and second order vanish in the zeros of f.

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  • In mathematical analysis, Glaeser's continuity theorem is a characterization of the continuity of the derivative of the square roots of functions of class . It was introduced in 1963 by Georges Glaeser, and was later simplified by Jean Dieudonné. The theorem states: Let be a function of class in an open set U contained in , then is of class in U if and only if its partial derivatives of first and second order vanish in the zeros of f. (en)
  • Le théorème de Glaeser, en analyse mathématique, est une caractérisation de la continuité de la dérivée de la racine carrée des fonctions de classe C2. Il a été publié en 1963 par Georges Glaeser, puis simplifié par Jean Dieudonné. Théorème de Glaeser — Soit une fonction de classe C2 sur un ouvert U de . Alors est de classe C1 sur U si et seulement si ses dérivées partielles d'ordre 1 et 2 s'annulent aux zéros de . (fr)
  • Em análise matemática, o teorema de Glaeser, é uma caracterização da continuidade da derivada da raiz quadrada das funções de classe (enésima derivada é uma função contínua). Foi publicado em 1963 por Georges Glaeser, e posteriormente simplificado por Jean Dieudonné. Teorema de Glaeser — Seja uma função de classe num conjunto aberto U contido em , então é de classe em U se e somente se suas derivadas parciais de ordens 1 e 2 desaparecem nos zeros de f. (pt)
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  • In mathematical analysis, Glaeser's continuity theorem is a characterization of the continuity of the derivative of the square roots of functions of class . It was introduced in 1963 by Georges Glaeser, and was later simplified by Jean Dieudonné. The theorem states: Let be a function of class in an open set U contained in , then is of class in U if and only if its partial derivatives of first and second order vanish in the zeros of f. (en)
  • Le théorème de Glaeser, en analyse mathématique, est une caractérisation de la continuité de la dérivée de la racine carrée des fonctions de classe C2. Il a été publié en 1963 par Georges Glaeser, puis simplifié par Jean Dieudonné. Théorème de Glaeser — Soit une fonction de classe C2 sur un ouvert U de . Alors est de classe C1 sur U si et seulement si ses dérivées partielles d'ordre 1 et 2 s'annulent aux zéros de . (fr)
  • Em análise matemática, o teorema de Glaeser, é uma caracterização da continuidade da derivada da raiz quadrada das funções de classe (enésima derivada é uma função contínua). Foi publicado em 1963 por Georges Glaeser, e posteriormente simplificado por Jean Dieudonné. Teorema de Glaeser — Seja uma função de classe num conjunto aberto U contido em , então é de classe em U se e somente se suas derivadas parciais de ordens 1 e 2 desaparecem nos zeros de f. (pt)
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  • Théorème de Glaeser (fr)
  • Glaeser's continuity theorem (en)
  • Teorema de Glaeser (pt)
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