The goal of this work is to extend the concepts of generalized Lelong number of positive currents investigated by Skoda, Demailly and Ghiloufi in complex analysis, to weakly positive supercurrents on the real superspaces. We generalize then a result of Lagerberg when the supercurrent is closed as well as a very recent result of Berndtsson for minimal supercurrents associated to submanifolds of ${\mathbb{R}}^n$. The main tool is a variant of the well-known Lelong–Jensen formula in the superformalism case. Moreover, we extend to our setting various interesting theorems in complex analysis such as Demailly and Rashkovskii comparison theorems. We also complete the work begun by Lagerberg on the degree of positive closed supercurrents and we prove a removable singularities result for positive supercurrents.

这项工作的目的是将由Skoda，Demailly和Ghiloufi在复杂分析中研究的广义Lelong正电流的概念扩展到实际超空间上的弱正超电流。然后，我们概括了超电流关闭时的Lagerberg结果以及Berndtsson的最新结果，即与超子流形相关的最小超电流。${\mathbb{[R}}^{ñ}$。在超形式主义情况下，主要工具是著名的Lelong-Jensen公式的变体。此外，我们扩展了我们在复杂分析中的各种有趣定理，例如Demailly和Rashkovskii比较定理。我们还完成了Lagerberg开始的关于正闭合超电流的程度的工作，并且我们证明了正超电流的可移除奇点结果。