cours/suite de fonctions convergente.md

up:: suite de fonctions title:: #maths/analyse

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[!definition] suite de fonctions convergente Soit (f_{n}) une suite de fonctions de I \subset \mathbb{R} \to \mathbb{R} On dit que f converge (simplement) vers f sur $I$ ssi : \boxed{\forall \varepsilon>0, \quad \forall x \in I, \quad \exists \eta _{x} \in \mathbb{N}, \quad \forall n \geq \eta _{x}, \quad |f_{\eta _{x}}(x) - f(x)| \leq \varepsilon} ^definition

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