Convergence in capacity

Pham Hoang Hiep. "Convergence in capacity." Annales Polonici Mathematici 93.1 (2008): 91-99. <http://eudml.org/doc/280871>.

@article{PhamHoangHiep2008,
abstract = {We prove that if $(Ω) ∋ u_j → u ∈ (Ω)$ in Cₙ-capacity then $lim inf_\{j→ ∞\}(dd^cu_j)^\{n\} ≥ 1_\{u>-∞\}(dd^cu)^\{n\}$. This result is used to consider the convergence in capacity on bounded hyperconvex domains and compact Kähler manifolds.},
author = {Pham Hoang Hiep},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic function; capacity; Monge-Ampére operator},
language = {eng},
number = {1},
pages = {91-99},
title = {Convergence in capacity},
url = {http://eudml.org/doc/280871},
volume = {93},
year = {2008},
}

TY - JOUR
AU - Pham Hoang Hiep
TI - Convergence in capacity
JO - Annales Polonici Mathematici
PY - 2008
VL - 93
IS - 1
SP - 91
EP - 99
AB - We prove that if $(Ω) ∋ u_j → u ∈ (Ω)$ in Cₙ-capacity then $lim inf_{j→ ∞}(dd^cu_j)^{n} ≥ 1_{u>-∞}(dd^cu)^{n}$. This result is used to consider the convergence in capacity on bounded hyperconvex domains and compact Kähler manifolds.
LA - eng
KW - plurisubharmonic function; capacity; Monge-Ampére operator
UR - http://eudml.org/doc/280871
ER -