0
$\begingroup$

If $f_n = 0$ a.e. for all $n \in \mathbb{N}$, does $\sum f_n \rightarrow 0$ uniformly a.e. to 0 as well?

  • 1
    Uniformly, no. Say for example all $f_n$ are $1$ on the rationals and $0$ on the irrationals.2012-12-20
  • 0
    @GEdgar: the asker just asked for uniformly a.e. (in the text of the question; the title seems to ask something else).2012-12-20
  • 0
    @user1770201: do you mean that the series converges uniformly and the limit is 0 a.e., or that the series converges uniformly a.e. to 0?2012-12-20

1 Answers 1