Capacity associated to a positive closed current
Dabbek KhalifaDépartement de Math Département de Math Faculé de sciences de Gab`es Faculé de sciences Monastir 6071 Gab`es Tunisie 5000 Monastir Tunisie
Elkhadhra FredjDépartement de Math Département de Math Faculé de sciences de Gab`es Faculé de sciences Monastir 6071 Gab`es Tunisie 5000 Monastir Tunisie
Let be an open set of and be a positive closed current of dimension on , we define a capacity associated to by: where is a compact set of . We prove, in the same way as Bedford-Taylor, that a locally bounded plurisubharmonic function is quasi-continuous with respect to . In the second part we define the convergence relatively to and we prove that if is a family of locally uniformly bounded plurisubharmonic functions and is a locally bounded plurisubharmonic function such that relatively to then in the current sense.
Cite this article
Dabbek Khalifa, Elkhadhra Fredj, Capacity associated to a positive closed current. Doc. Math. 11 (2006), pp. 469–486DOI 10.4171/DM/219