In this paper, we show the existence of the Lelong–Demailly numbers of positive S-plurisubharmonic currents. Moreover, a valid definition of \(\mathrm{{dd}}^{c}g \wedge T\) is obtained for plurisubharmonic currents T and unbounded plurisubharmonic functions g. The importance of this definition comes from the sharpness of our condition on the Hausdorff dimension of the locus points of g.

中文翻译：

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S-Plurisubahronic 电流的 Lelong–Demailly 数和楔积

在本文中，我们证明了正S多次谐波电流的 Lelong-Demailly 数的存在。此外，对于多次谐波电流T和无界多次谐波函数g ，获得了\(\mathrm{{dd}}^{c}g \wedge T\)的有效定义。这个定义的重要性来自于我们在g的轨迹点的 Hausdorff 维上的条件的尖锐性。