27 lines
1.1 KiB
Markdown
27 lines
1.1 KiB
Markdown
---
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alias: [ "convergence uniforme", "uniformément convergente", "convergence uniforme d'une suite de fonctions", "suite de fonctions uniformément convergente", "uniformément convergente" ]
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---
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up:: [[suite de fonctions convergente]]
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title:: "$(f_{n})$ CVU ssi : $\lim\limits_{ n \to +\infty } \sup\limits_{x \in I} \left| f_{n}(x) - f(x) \right| = 0$ où $f = \lim\limits_{ n \to \infty }f_{n}$"
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#maths/analyse
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---
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> [!definition] fonction uniformément convergente
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> Soit $(f_{n})$ une suite de fonctions de $I \subset \mathbb{R} \to \mathbb{R}$
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> On dit que $(f_{n})$ est **uniformément convergente vers $f$ sur $I$** ssi :
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> $\boxed{\forall \varepsilon > 0, \quad \exists n_0 \in \mathbb{N}, \quad \forall x \in I, \quad \forall n \geq n_0, \quad |f_{n}(x)-f(x)| \leq \varepsilon}$
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^definition
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> [!query] Sous-notes de `=this.file.link`
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> ```dataview
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> LIST title
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> FROM -#cours AND -#exercice AND -"daily" AND -#excalidraw AND -#MOC
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> WHERE any(map([up, up.up, up.up.up, up.up.up.up], (x) => econtains(x, this.file.link)))
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> WHERE file != this.file
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> SORT up!=this.file.link, up.up.up.up, up.up.up, up.up, up
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> ```
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