1 Introduction ................................................. 5
2 Preliminaries ................................................ 8
3 The domain of definition of the complex Monge-Ampère
operator .................................................... 13
4 Maximal plurisubharmonic functions .......................... 22
5 The comparison principle .................................... 29
6 The Dirichlet problem ....................................... 37
6.1 Regular measures ....................................... 37
6.2 Singular measures ...................................... 43
6.3 The general case ....................................... 46
7 Generalized boundary values ................................. 50
7.1 Monge-Ampère boundary measures ......................... 51
7.2 Stability of solutions and the complex Monge-Ampère
type equation .......................................... 56
7.3 Subextension ........................................... 63
8 The homogeneous Dirichlet problem for pluriharmonic
functions ................................................... 67
References ..................................................... 78
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