# Article

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Keywords:
positive current; plurisubharmonic function; plurisubharmonic current
Summary:
We discuss the existence of the current $g^{k}T$, $k \in \mathbb N$ for positive and closed currents $T$ and unbounded plurisubharmonic functions $g$. Furthermore, a new type of weighted Lelong number is introduced under the name of weight $k$ Lelong number.
References:
[1] Abdulaali, A. K. Al: The inductive wedge product of positive currents. J. Math. Anal. Appl. 412 (2014), 744-755. DOI 10.1016/j.jmaa.2013.10.072 | MR 3147245 | Zbl 1314.32049
[2] Abdulaali, A. K. Al, Mir, H. El: The existence problem of $S$-plurisubharmonic currents. C. R. Math., Acad. Sci. Paris 353 (2015), 605-610. DOI 10.1016/j.crma.2015.04.011 | MR 3352030 | Zbl 1321.32011
[3] Bishop, E.: Conditions for the analyticity of certain sets. Mich. Math. J. 11 (1964), 289-304. DOI 10.1307/mmj/1028999180 | MR 0168801 | Zbl 0143.30302
[4] Demailly, J.-P.: Monge-Ampère operators, Lelong numbers and intersection theory. Complex Analysis and Geometry University Series in Mathematics, Plenum Press, New York (1993), 115-193. DOI 10.1007/978-1-4757-9771-8_4 | MR 1211880 | Zbl 0792.32006
[5] ss, J. E. Fornæ, Sibony, N.: Oka's inequality for currents and applications. Math. Ann. 301 (1995), 399-419. DOI 10.1007/BF01446636 | MR 1324517 | Zbl 0832.32010
[6] Shiffman, B.: On the removal of singularities of analytic sets. Mich. Math. J. 15 (1968), 111-120. DOI 10.1307/mmj/1028999912 | MR 0224865 | Zbl 0165.40503

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