Matroid valuation on independent sets (Q1354118)

Recently \textit{A. W. M. Dress} and \textit{W. Wenzel} [Adv. Math. 93, No. 2, 214-250 (1992; Zbl 0754.05027)] introduced the concept of valuated matroid in terms of a quantitative extension of the basis exchange axiom for matroids. This paper gives two sets of cryptomorphically equivalent axioms of valuated matroids in terms of a function defined on the family of the independent sets of the underlying matroid.