Hi!
I am having trouble interpreting the notation on this question, 
What does lim sup n mean in this context?
I also do not quite understand the max norm, is it supposed to be sup(f_n(x)) and not sup(f(x))? Because if it is correctly written, isn't it just a fix value for all n?
You're right that it should be ![||f_n||_\infty = \sup_{x\in [0,1]} |f_n(x)|](https://kurser.math.su.se/filter/tex/pix.php/4c72297b15c53c009351127fb1263692.png "||f_n||_\infty = \sup_{x\in [0,1]} |f_n(x)|")
. Definition 3.16 in Rudin defines 
, it doesn't have any different meaning in this context.
. Definition 3.16 in Rudin defines , it doesn't have any different meaning in this context.