Equlibrium measure of a product subset of ℂⁿ

Author:

Błocki Zbigniew

Abstract

In this note we show that an equilibrium measure of a product of two subsets of C n {\mathbb {C}}^{n} and C m {\mathbb {C}}^{m} , respectively, is a product of their equilibrium measures. We also obtain a formula for ( d d c max { u , v } ) p (dd^{c}\max \{u,v\})^{p} , where u , v u,v are locally bounded plurisubharmonic functions and 2 p n 2\leq p\leq n .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference7 articles.

1. A new capacity for plurisubharmonic functions;Bedford, Eric;Acta Math.,1982

2. The complex equilibrium measure of a symmetric convex set in 𝑅ⁿ;Bedford, Eric;Trans. Amer. Math. Soc.,1986

3. Product property of the relative extremal function;Edigarian, Armen;Bull. Polish Acad. Sci. Math.,1997

4. London Mathematical Society Monographs. New Series;Klimek, Maciej,1991

5. [Sa] A.Sadullaev, Plurisubharmonic measures and capacities on complex manifolds, Russian Math.Surveys 36 (1981), 61-119.

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