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Real Analysis/Pointwise Convergence
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Pointwise Convergence
Generalized Integration
Uniform Convergence
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Let be a sequence of functions defined on a common domain . Then we say that converges pointwise to a function if for each the numerical sequence converges to . More precisely speaking:
For any and for any , there exists an N such that for any n>N,
An example:
The function
converges to the function
This shows that a sequence of continuous functions can pointwise converge to a discontinuous function.
pt:Análise real/Índice/Convergência pontual