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

Let X and Y be non-empty sets, E 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 E and ν on F is continuous on the product field generated by E and F whenever μ is continuous and ν is compact. A similar result holds for the compactness of indirect product measures.