- #1
AxiomOfChoice
- 533
- 1
My functional analysis professor made the following assertion the other day: If [itex]f_n \to f[/itex] in the [itex]L^2[/itex] norm, then there is a subsequence [itex]f_{n_k}[/itex] that converges pointwise almost everywhere to [itex]f[/itex]. This is the first I've heard of that...can someone point me to a proof of this proposition? Does it have a name?