## continuety and convergence question

suppose f_n(x) is continues and periodic
suppose fn(x) converges to f(x) in L1(T) does f(x) has to be continues
??

how i tried:
||fn-f||_{L1(T)} is an integral from -pi to pi on |fn-f|
i know that if there is a finite number of discontinuety points in a function ,then the integral over it will be the same as a continues function

so i dont know
if its true or nor