When is $f(x_1, x_2, ldots , x_n) = u_1 (x_1) + u_2(x_2) + cdots + u_n (x_n)$?

[摘要] We discuss subsets 𝑆 of $mathbb{R}^n$ such that every real valued function 𝑓 on 𝑆 is of the form$$f(x_1, x_2, ldots , x_n) = u_1(x_1) + u_2(x_2) + cdots + u_n (x_n),$$and the related concepts and situations in analysis.

[学科分类] 数学（综合）

[关键词] Good set;sequentially good set;linked component;sequentially good measure;simplicial measure.