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Convergence of Functions

  • Rinaldo B. Schinazi
Chapter
  • 830 Downloads

Abstract

Let (fn) be a sequence of functions converging to some function f. Here are a few questions we are interested in.

If the fn are continuous, is f continuous?

If the fn are differentiable, is f differentiable?

References

  1. W. Dunham, The Calculus Gallery (Princeton University Press, Princeton, 2005)CrossRefGoogle Scholar
  2. W. Feller, An Introduction to Probability Theory and Its Applications, vol. II, 2nd edn. (Wiley, New York, 1971)Google Scholar
  3. S. Krantz, Real Analysis and Foundations (CRC Press, Boca Raton, 1991)zbMATHGoogle Scholar
  4. R.B. Schinazi, From Calculus to Analysis (Birkhauser, Boston, 2011)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Rinaldo B. Schinazi
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoColorado SpringsUSA

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