Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli

  • Jürgen Jost
Part of the Universitext book series (UTX)


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.


Banach Space Differentiable Function Limit Function Uniform Convergence Bounded Interval 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jürgen Jost
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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