Geometric Criteria For Removable Sets

摘要

The paper presents some exact geometric characteristics of removable sets for two classes of weighted capacities. Bibliography: 5 titles.rnLet G be an open set in R~n, n ≥ 2, and let H_k and L_k be the fc-dimensional Hausdorff and Lebesgue measures, respectively, 1 ≤ k ≤ n. Let a system of coordinates Ox_1x_2... x_n in R~n be given. Define the n-dimensional cells as the sets {x : a_i < x_i < b_i,i = 1, 2,...,n} for some positive reals a_i and b_i, i = 1,2,... ,n. The sets that are connected unions of a finite number of cells are called cell sets.