Let ɸ be a given set of real-valued functions on the set T and let ß: ɸ → R given functional with values in the extended real line R = [−∞, ∞]. The objective of the paper is to construct contents or measures μ with good regularity and smoothness properties satisfying the integral inequalities ∫*φ dμ ≤ ß (φ), where ∫*denotes the upper integral.
