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→Properties: [Properties] Typo. Tags: Mobile edit Mobile web edit |
→Properties: [Properties] Tags: Mobile edit Mobile web edit |
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:* if <math>f_1</math> and <math>f_2</math> are plurisubharmonic functions, then the sum <math>f_1+f_2</math> is a plurisubharmonic function.
*Plurisubharmonicity is a local property, i.e. a function is plurisubharmonic if and only if it is plurisubharmonic in a neighborhood of each point.
*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 is plurisubharmonic.
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