%0 Journal Article
%T Kolodziej's subsolution theorem for unbounded pseudoconvex domains
%A Åhag, Per
%A Czyż, Rafał
%J Universitatis Iagellonicae Acta Mathematica
%V 2012
%R 10.4467/20843828AM.12.001.1119
%N Tom 50
%P 7-23
%K Complex Monge-Ampère  operator, plurisubharmonic function, Dirichlet problem
%@ 0083-4386
%D 2013
%U https://ejournals.eu/czasopismo/universitatis-iagellonicae-acta-mathematica/artykul/kolodziejs-subsolution-theorem-for-unbounded-pseudoconvex-domains
%X 
	In this paper we generalize Kolodziej's subsolution theorem to bounded and unbounded pseudoconvex domains, and in that way we are able to solve complex Monge-Ampère equations on general pseudoconvex domains. We then give a negative answer to a question of Cegrell and Kolodziej by constructing a compactly supported Radon measure µ that vanishes on all pluripolar sets in Cn such that µ(Cn) = (2π)n, and forwhich there is no function u in L+ such that (ddcu)=µ. We end this paper by solving a Monge-Ampère type equation. Furthermore, we proveuniqueness and stability of the solution.