On the differences and sums of periodic measurable functions
Author constructs two measurable periodic functions such that their sums are continuous and unbounded. This gives a negative answer to the question from the article by \textit{M. Laczkovich} and \textit{Sz. Révész} [Acta Math. Hung. 54, No. 3/4, 329-341 (1989; Zbl 0725.26004)] whether if \(f\) is continuous and has a measurable \((\alpha_1,\dots,\alpha_n)\)-decomposition then it also has a continuous \((\alpha_1,\dots,\alpha_n)\)-decomposition. Recall that \(f=f_1+\dots+f_n \) is \((\alpha_1,\dots,\alpha_n)\)-decomposition of \(f\) if \(f_i\) is periodic modulo \(\alpha_i\) for every \(i=1,\dots,n\).
scientific article; zbMATH DE number 1355168