Essential supremum and supremum of summable functions

Let D ≌ RN , 0 0}, where ess sup ƒ denotes the essential supremum of ƒ. These properties can be used for computing ess sup ƒ. As example, two algorithms are stated. If the function ƒ is dense, or lower semicontinuous, or if −ƒ is robust, then sup ƒ = ess sup ƒ. In this case, the algorithms mentioned can be applied for determining the supremum of ƒ, i.e., also the global maximum of ƒ if it exists.