We note that the well-known result of von Neumann (Contrib Theory Games 2:5–12, 1953) is not valid for all doubly substochastic operators on discrete Lebesgue spaces ℓp(I), p∈[1,∞). This fact lead us to distinguish two classes of these operators. Precisely, the class of increasable doubly substochastic operators on ℓp(I)is isolated with the property that an analogue of the Von Neumann result on operators in this class is true. The submajorization relation ≺son the positive cone ℓp(I)+, when p∈[1,∞), is introduced by increasable substochastic operators and it is provided that submajorization may be considered as a partial order. Two different shapes of linear preservers of submajorization ≺son ℓ1(I)+and on ℓp(I)+, when Iis an infinite set, are presented.