Definition of Strong Convergence in $L^p$

Question

Is strong convergence in $L^p$, ie $f_i \overset{strongly}\longrightarrow$, just $||f_i-f||_{L^p} \rightarrow 0$. If so why dont we just call it convergence?

Answer 1

Yes your definition is correct. Usually people do simply say convergence, but if you want to really emphasise that you do not mean another form of convergence e.g. weak convergence or almost everywhere convergence, you can use the word strong.