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  • Examples and counter-examples in analysis
  • Pointwise convergence

Examples and counter-examples in analysis

Author:
Vincent Pantaloni
Topic:
Continuity, Functions, Function Graph, Limits, Piecewise Functions, Power Functions, Sequences and Series, Trigonometric Functions
Animations to illustrate lessons in analysis
Examples and counter-examples in analysis

Table of Contents

  • Pointwise convergence

    • Boundedness is not preserved by pointwise convergence.
    • Continuity is not preserved by pointwise convergence.
    • Differentiability is not preserved by pointwise convergence.
    • fn converges does not imply f'n converges
    • Integration counter-examples : Witch's hat functions
    • Integration and uniform convergence
Next
Boundedness is not preserved by pointwise convergence.

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