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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
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
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