Ghalb, Mohammed Abduljleel Abdoh2022-05-182022-05-182015755https://drepo.sdl.edu.sa/handle/20.500.14154/3389this thesis concerns the extension of positive currents across a closed obstacle which has a small housdorff dimension. in this thesis , important properties of positive currents , plurisubharmonic functions and hausdorff measure are summarized the main roiginality in this work consists of the following.enThesis