If we have that:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f_T \left( x \right) \to f\left( x \right)[/tex] for each x (pointwise convergence)

and also that:

[tex]f_T[/tex] and [tex]f[/tex] are bounded or/and uniformly continuous functions then can we show that there is also uniform convergence?

If no why not? Can you show it with an example?

In general, are there any cases where pointwise convergence implies uniform convergence? I can't find any proof on that. Can you guide me on this?

Thanks in advance

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Pointwise => uniform convergence when?

**Physics Forums | Science Articles, Homework Help, Discussion**