7
$\begingroup$

My question is: For $f_n, g, h \in L^p(X)$, where $X$ is a finite measure space, if $f_n$ converges to $g$ a.e and $f_n$ converges to $h$ weakly in $L^p$, can we conclude any relationship between $g$ and $h$? Thanks!

  • 3
    Welcome to math.stackexchange! What does "$g$ converge to $h$" mean? Usually, we talk about convergence for a sequence (or a net), not for a single function.2012-01-25
  • 0
    Thanks, Davide! I have edited the question.2012-01-25
  • 1
    On which measured space do you work?2012-01-25
  • 1
    On any finite measure space.2012-01-25

2 Answers 2