# Convergence in Capacity

Yang Xing^{[1]}

- [1] Swedish University of Agricultural Sciences Centre of Biostochastics 901 83 Umeå(Sweden)

Annales de l’institut Fourier (2008)

- Volume: 58, Issue: 5, page 1839-1861
- ISSN: 0373-0956

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topXing, Yang. "Convergence in Capacity." Annales de l’institut Fourier 58.5 (2008): 1839-1861. <http://eudml.org/doc/10364>.

@article{Xing2008,

abstract = {We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity $C_n$ of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity $C_\{n-1\}$ of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampère equations.},

affiliation = {Swedish University of Agricultural Sciences Centre of Biostochastics 901 83 Umeå(Sweden)},

author = {Xing, Yang},

journal = {Annales de l’institut Fourier},

keywords = {the complex Monge-Ampère operator; plurisubharmonic function; capacity; plurisubharmonic functions; Monge-Ampère operator; capacities},

language = {eng},

number = {5},

pages = {1839-1861},

publisher = {Association des Annales de l’institut Fourier},

title = {Convergence in Capacity},

url = {http://eudml.org/doc/10364},

volume = {58},

year = {2008},

}

TY - JOUR

AU - Xing, Yang

TI - Convergence in Capacity

JO - Annales de l’institut Fourier

PY - 2008

PB - Association des Annales de l’institut Fourier

VL - 58

IS - 5

SP - 1839

EP - 1861

AB - We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity $C_n$ of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity $C_{n-1}$ of functions in some case. As applications we give certain stability theorems of solutions of Monge-Ampère equations.

LA - eng

KW - the complex Monge-Ampère operator; plurisubharmonic function; capacity; plurisubharmonic functions; Monge-Ampère operator; capacities

UR - http://eudml.org/doc/10364

ER -

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