Convergence in capacity

Pham Hoang Hiep¹

¹ Department of Mathematics Hanoi University of Education (Dai Hoc Su Pham HaNoi) Cau Giay, Hanoi, VietNam

Annales Polonici Mathematici, Tome 93 (2008) no. 1, pp. 91-99.

Résumé

We prove that if $\mathcal{E}(\Omega )\ni u_j\to u\in \mathcal{E}(\Omega )$ in $C_n$-capacity then ${\mathrm{l}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{f}}_{j\to \mathrm{\infty }}(d{d}^c{u}_j{)}^n\ge 1_{\{u>-\mathrm{\infty }\}}(d{d}^{c}u{)}^n$. This result is used to consider the convergence in capacity on bounded hyperconvex domains and compact Kähler manifolds.

Détail

DOI : 10.4064/ap93-1-8

Mots-clés : prove mathcal mit omega mathcal mit omega n capacity mathop lim inf infty geq infty result consider convergence capacity bounded hyperconvex domains compact hler manifolds