Measurable Hermitian-positive functions

Let , respectively, denote the sets of continuous, measurable, and almost-everywhere vanishing functions f(x) (–a<x<a; f(0)>0). The theorem is proved that for every there correspond and , such that f=f_c + f_s. Some unsolved problems related to this theorem are formulated.Translated from Matematicheskie Zametki, Vol. 23, No. 1, pp. 79–89, January, 1978.