A vector space may be given a partial order ≤ ≤ , under which some vectors can be compared. For example, n -dimensional real space R n can be ordered by comparing its vectors componentwise. Ordered vector spaces, for example Riesz spaces, are fundamental to Lebesgue integration, which relies on the ability to express a function as a difference of two positive functions f = f + − − f − − . where f + denotes the positive part of f and f − − the negative part.