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*If <math>f</math> is plurisubharmonic and <math>\varphi:\mathbb{R}\to\mathbb{R}</math> an increasing convex function then <math>\varphi \circ f</math> is plurisubharmonic. (<math>\varphi(-\infty)</math> is interpreted as <math>\lim_{x \rightarrow -\infty} \varphi(x)</math>.)
*If <math>f_1</math> and <math>f_2</math> are plurisubharmonic functions, then the function <math>\max(f_1,f_2)</math> is plurisubharmonic.
*The pointwise limit of a decreasing sequence of plurisubharmonic functions is plurisubharmonic.
*Every continuous plurisubharmonic function can be obtained as the limit of a decreasing sequence of smooth plurisubharmonic functions. Moreover, this sequence can be chosen uniformly convergent.<ref>R. E. Greene and H. Wu, ''<math>C^\infty</math>-approximations of convex, subharmonic, and plurisubharmonic functions'', Ann. Scient. Ec. Norm. Sup. 12 (1979), 47–84.</ref>
*The inequality in the usual [[semi-continuity]] condition holds as equality, i.e. if <math>f</math> is plurisubharmonic then <math>\limsup_{x\to x_0}f(x) =f(x_0)</math>.
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