We show that ω0(X)=limT→∞limε→0ωT(X,ε) is a measure of noncompactness defined on some subsets of the space C(R+)={x:R+→R,xcontinuous} furnished with the distance defined by the family of seminorms ∣x∣n. Moreover, using a technique associated with the measures of noncompactness, we prove the existence of solutions of a quadratic Urysohn integral equation on an unbounded interval. This measure allows to obtain theorems on the existence of solutions of a integral equations on an unbounded interval under a weaker assumptions then the assumptions of theorems obtained by applying two-component measures of noncompactness