Convergence in capacity and applications

  • Pham Hoang Hiep

Abstract

In this article we prove that if $u_j, v_j, w\in\mathcal{E}(\Omega)$ such that $u_j,v_j\geq w$, $\forall\ j\geq 1$, and $|u_j-v_j|\to 0$ in $C_n$-capacity, then $\lim_{j\to\infty}h(\varphi_1,\ldots,\varphi_m) [(dd^cu_j)^n-(dd^cv_j)^n]=0$ in the weak-topology of measures for all $\varphi_1,\ldots ,\varphi_m\in{\operatorname{PSH}}\cap L_{\operatorname {loc}}^\infty (\Omega)$, $h\in C(\mathsf{R}^m)$. We shall then use this result to give some applications.
Published
2010-09-01
How to Cite
Hiep, P. H. (2010). Convergence in capacity and applications. MATHEMATICA SCANDINAVICA, 107(1), 90-102. https://doi.org/10.7146/math.scand.a-15144
Section
Articles