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[SOLVED] pointwise convergence

Fermat

Active member
Nov 3, 2013
188
Does pointwise convergence mean that |$f_{n}$-$f$|->0 for each x?
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,725
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

Well-known member
Feb 13, 2012
1,704
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

$\chi$ $\sigma$