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A New Capacity In The Class Of ShM Functions Defined By Laplace Operator, Nurali Akramov, Khakimboy Egamberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we define a new capacity Δ_m on the class of sh_m functions, which is defined by Laplace operator. We prove that Δ_m-capacity satisfies Choquet’s axioms of measurability. Moreover, we compare our capacity with Sadullaev-Abdullaev capacities. In particular, it implies that Δ_m-capacity of a set E is zero if and only if E is a m-polar set.