# Decreasing sequence of subharmonic functions

1. Aug 9, 2009

### jian1

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.