Der Kolmogoroff'sche Darstellungsatz bei halbstetigen Funktionen (Q1062162)

The result is the following: Not every semicontinuous f(x,y) is representable via a given \(H_ q(x,y),\quad 1\leq q\leq m,\) in the form: \(f(x,y)=\sum^{m}_{q=1}g_ q(H_ q(x,y)),\) where \(g_ q\) is a function of the first class. \{Reviewer's remark: This result, in spite of the title, is only remotely related to the Kolmogorov representation theorem \(f(x,y)=\sum^{2m+1}_{q=1}g_ q(\sum^{m}_{p=1}H_{p,q}(x_ p)),\) with all the functions continuous and the \(H_{p,q}\) depending on the natural number m.\}