Limsup/inf of sequences of functions Does anyone have a good, intuitive explanation for what the $\limsup$ and $\liminf$ of a sequence of functions is? So, if I have a sequence of functions $f_n(x)$, what is the $\limsup$ of that sequence?
I am particularly looking at the sequence $f_n = n \cdot \chi_{[1/n,2/n]}$, but am really interested in seeing a more general explanation.

Perhaps a graphical visualization of these two concepts would be helpful:

As for your function sequence, it looks something like

Clearly both limits are zero: $\limsup \,f_n = 0$, $\liminf \,f_n = 0$.
