Let C be the space of all middle Cantor sets, it is shown that for a dense subset L of C × C × ℝ, set Cα − λCβ forms a uniformly contracting self-similar set when (Cα, Cβ, λ) ∈ L. By selecting an appropriate element (CαCβ, λ) ∈ L, we see that Cα − λCβ does not satisfy open set condition and then we calculate its Lebesgue measure that is zero.