Abstract: An integral optimality condition for global optimization problem is investigated by using a level set auxiliary function. The auxiliary function has one variant that represents an estimated optimal value of the objective function in primal optimization problem and one controlling parameter for accuracy. Necessary and sufficient condition for global optimality in terms of the behavior of the auxiliary function is derived. The integral global optimality condition is obtained via a limiting process of this auxiliary function. Furthermore, if the measure is the Lebesgue measure and the integral region takes a finite subset of the Natural Number set, then this integral global optimality condition divergences to the approximation scheme that used aggregate function to approximate the max-function in the finite minimax problem. So the integral global optimality condition is an extension of this approximation scheme in continuous maximum problem.