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Constructions of contents and measures satisfying a prescribed set of integral inequalities

Hoffmann-Jørgensen J.

Probability and Mathematical Statistics

2006

Vol. 26, Fasc. 2

283--313

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.