Subharmonic function: Difference between revisions

Revision as of 18:32, 26 November 2016

Revision as of 17:46, 15 December 2016

Line 23:

*The pointwise maximum of two subharmonic functions is subharmonic.

*The limit of a decreasing sequence of subharmonic functions is subharmonic (or identically equal to <math>-\infty</math>).

*Subharmonic functions are not necessarily continuous in the usual topology, however one can introduce the [[fine topology]]{{dn (potential theory)|date=Novemberfine 2016}}topology]] which makes them continuous.

==Examples==

If <math>f</math> is [[analytic function|analytic]] then <math>\log|f|</math> is subharmonic. More examples can be constructed by using the properties listed above,

by taking maxima, convex combinations and limits. In dimension 1, all subharmonic functions can be obtained in this way.