I am trying to understand an exercise about distributions. In this exercise I am given locally integrable functions $f_n$ and $f$.
Assuming that $f_n$ are in $L^p$ for $1\leq p\leq \infty$, and $f_n\to f$ weakly in $L^p$, I want to prove that $f_n\to f$ as distributions. But I'm not sure how should I interpret that $f_n\to f$ weakly in $L^p$.