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Decreasing sequence of subharmonic functions

  1. Aug 9, 2009 #1
    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.
  2. jcsd
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