1. The problem statement, all variables and given/known data As part of a larger proof, I'm trying to show that ||fn|| --> ||f|| implies <fn> --> f in Lp, where <fn> is a sequence of functions in Lp, 1≤p<∞, which converge a.e. to a function f in Lp. 2. Relevant equations ||f|| = (∫|f|p)1/p. 3. The attempt at a solution There's some string of inequalities I need to obtain ||f-fn||≤|||f||-||fn|||<∂. Any ideas?