Abstract In Shulman (J Funct Anal 263:1468–1484, Theorem 2.2) the author estimated cardinality of global image a subadditive map from group to an arbitrary power set and applied result functional equations Levi-Civita type (the relations this covering by subgroups will be shortly discussed in present paper). Here we establish metric stability theorem. Namely it shown that if set-valued F G spac...