Abstract: This article is committed to deal with measure of non-compactness of operators in Banach spaces. Firstly, the collection C(X) (consisting of all nonempty closed bounded convex sets of a Banach space X endowed with the uaual set addition and scaler multiplication) is a normed semigroup, and the mapping J from C(X) onto F(Ω) is a fully order-preserving positively linear surjective isometry, where Ω is the closed unit ball of X^* and F(Ω) the collection of all continuous and w^*-lower semicontinuous sublinear functions on X^* but restricted to Ω. Furthermore, both E_C=JC-JC and E_K=JK-JK are Banach lattices and E_K is a lattice ideal of E_C. The quotient space E_C/E_K is an abstract M space, hence, order isometric to a sublattice of C(K) for some compact Haudorspace K, and (FQJ)C which is a closed cone is contained in the positive cone of C(K), where Q:E_C → E_C/E_K is the quotient mapping and F:E_C/E_K → C(K) is a corresponding order isometry. Finally, the representation of the measure of non-compactness of operators is given:Let B_X be the closed unit ball of a Banach space X, then
μ(T)=μ(T(B_X))=||(F QJ)T(BX)||_C(K), ∀T ∈ B(X).

Key words: Measure of non-compactness, measure of non-compactness of operators, Banach lattice, Banach space