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Erschienen in:
1998 | OriginalPaper | Buchkapitel
Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli
verfasst von : Jürgen Jost
Erschienen in: Postmodern Analysis
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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We introduce the notion of uniform convergence. This leads to Banach spaces of continuous and differentiable functions. We discuss when the limit of the derivatives of a convergent sequence of functions equals the derivative of the limit and related questions. The theorem of Arzela-Ascoli is shown, saying that an equicontinuous and uniformly bounded sequence of functions on a closed and bounded set contains a uniformly convergent subsequence.