m-subharmonic functions on the projective space P<sup>n</sup>

We consider a class of quasi m-subharmonic functions in the projective space ℙn. Similarly to the m-subharmonic functions, we will show a number of potential properties of quasi m-subharmonic functions. We introduce the concepts of Green’s function Vqm*(z,K,ℙn), ��m-measure ωqm*(z,E,D) and study m-regularities of compact sets K ⊂ ℙn. In contrast to the complex space ℂn, we will prove that in the projective space ℙn the locally m-regularity of compact sets is equivalent to their global m-regularity.

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