- #1
mathmari
Gold Member
MHB
- 5,049
- 7
Hey!
If $f_n, f \in L^p, 1\leq p < +\infty$ and $f_n \rightarrow f$ almost everywhere, and $||f_n||_p \rightarrow ||f||_p$, then $f_n\rightarrow f$ as for the norm.
Could you give me some hints how to show it?? (Wondering)
What does convergence as for the norm mean?? (Wondering)
If $f_n, f \in L^p, 1\leq p < +\infty$ and $f_n \rightarrow f$ almost everywhere, and $||f_n||_p \rightarrow ||f||_p$, then $f_n\rightarrow f$ as for the norm.
Could you give me some hints how to show it?? (Wondering)
What does convergence as for the norm mean?? (Wondering)