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 μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar sets.

We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.

Dans cet article on montre que toute $f\in A^{\infty }(\bar{D})$ a une décomposition $f\left(z\right)-f\left(w\right)={\sum }_{i=1}^n{g}_i(z,w)(z_i-w_i)$ avec $g_i\in A^{\infty }(\overline{D\times D})$ pour les domaines pseudoconvexes à frontière réelle-analytique et aussi pour les domaines pseudoconvexes pour lesquels le résultat soit valable localement.