Real Analysis/Pointwise Convergence
|←Generalized Integration||Real Analysis
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 preciselly speaking:
For any and for any , there exists an N such that for any n>N,
converges to the function
This shows that a sequence of continuous functions can pointwise converge to a discontinuous function.