MHB Pointwise Conv. | Does $f_{n}$-$f$ -> 0 for Each x?

[Fermat1]

Does pointwise convergence mean that |$f_{n}$-$f$|->0 for each x?

 

[Opalg]

Does pointwise convergence mean that |$f_{n}$-$f$|->0 for each x?

Yes. More precisely, it means that for each $x$ (in some specified domain) $|f_n(x) - f(x)| \to0$ as $n\to\infty$.

 

[chisigma]

Does pointwise convergence mean that |$f_{n}$-$f$|->0 for each x?

Wellcome back to MHB Fermat!... yes, pointwise convergence to f(x) means that $\lim_{n \rightarrow \infty} |f_{n} (x) - f(x)| = 0$ for any x in the domain...

Kind regards

$\chi$ $\sigma$