Convergence in capacity
Volume 93 / 2008
Annales Polonici Mathematici 93 (2008), 91-99
MSC: Primary 32W20; Secondary 32U05.
DOI: 10.4064/ap93-1-8
Abstract
We prove that if ${\mathcal E}({\mit \Omega })\ni u_j\to u\in {\mathcal E}({\mit \Omega })$ in $C_n$-capacity then $\mathop {\rm lim\, inf}_{j\to \infty }(dd^cu_j)^n\geq 1_{\{ u>-\infty \} }(dd^cu)^n$. This result is used to consider the convergence in capacity on bounded hyperconvex domains and compact Kähler manifolds.
