1. The problem statement, all variables and given/known data Let u(z) be a continuous function from D to [-inf, inf) (In the extended field sense which includes -inf). Suppose u_n (z) is a decreasing sequence of subharmonic functions on D such that u_n converges to a function v pointwisely. Show that v(z) is subharmonic. 2. Relevant equations 3. The attempt at a solution I have proved that for such u_n (z) are increasing sequences , then v(z) is subharmonic, but encountered problem when the sequence is decreasing.