Abstract: An integral level set method for solving global optimization problems was propo sed in 1978 and improved in 1999.This method has only been used in continuous fu nctions in a closed domain.In this paper,the method is extended to bounded measu r able functions by introducing the concept of essential infimum and the property of Lebesgue integral.An integral level set conceptual algorithm is proposed for bounded measurable functions,and an optimality condition is obtained.

Key words: bounded mea surable functions, integral level set, optimality condition , global optimization