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# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Subextension of plurisubharmonic functions without changing the Monge–Ampère measures and applications

### Tom 112 / 2014

Annales Polonici Mathematici 112 (2014), 55-66 MSC: 32U05, 32U15, 32W20. DOI: 10.4064/ap112-1-5

#### Streszczenie

The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge–Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in $C_{n-1}$-capacity then the sequence of the Monge–Ampère measures of subextensions is weakly$^*$-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure $\mu$ in the class $\mathcal {F}(\varOmega ,g)$ without the assumption that $\mu$ vanishes on all pluripolar sets.

#### Autorzy

• Le Mau HaiDepartment of Mathematics
Hanoi National University of Education
Hanoi, Vietnam
e-mail
• Nguyen Xuan HongDepartment of Mathematics
Hanoi National University of Education
Hanoi, Vietnam
e-mail

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