Solution
= Solution
Working with measurable functions modulo equality almost everywhere, the sequence is Cauchy in <Lp space> if for every $\epsilon>0$ there exists $N$ such that $\|f_n-f_m\|_p<\epsilon$ for all $m,n\geq N$. This is a statement about integral <norm> distance, not pointwise convergence. Without quotienting null functions the displayed quantity is a seminorm, so the conventional $L^p$ normed space uses these equivalence classes.