Poincaré–Lelong formula, J-analytic subsets and Lelong numbers of currents on almost complex manifolds

In this paper, we first establish a Poincaré–Lelong type formula in the almost complex setting. Then, after introducing the notion of J  -analytic subsets, we study the restriction of a closed positive current defined on an almost complex manifold (M,J)(M,J) on a J-analytic subset. Finally, we prove that the Lelong numbers of a plurisubharmonic current defined on an almost complex manifold are independent of the coordinate systems.