On a measure of noncompactness in the space of functions with tempered increments

Based on a certain criterion for relative compactness in the space of functions with tempered increments, we construct a formula expressing a set function in that space. We prove that the mentioned function is a sublinear measure of noncompactness in the space in question. Moreover, we show that with help of that measure of noncompactness, we can obtain an existence result for a nonlinear quadratic integral equation of Hammerstein type in the space of function satisfying the Hölder condition.