Continuity and compactness of the indirect product of two non-additive measures

摘要

Let X and Y be non-empty sets, ε a field of subsets of X, and F a field of subsets of Y. Then, every uniformly autocontinuous indirect product of two non-additive measures μ on ε and v on F is continuous on the product field generated by ε and F whenever μ is continuous and v is compact. A similar result holds for the compactness of indirect product measures.