On some categorical properties of the functor \(U_R\) (Q1581945)

In \textit{T. O. Banakh} [Mat. Stud. 5, 65-87 and 88-106 (1995; Zbl 1023.28501 andZbl 1023.28502)] the functor \(P_R\) of Radon probability measures in the category \textit{Tych} of all Tychonoff spaces was studied. Recently, the author obtained similar results for the functor \(P_\beta\) of probability measures with compact support. In the present paper the unit ball \(U_R(X)\) of nonnegative Radon measures on a Tychonoff space \(X\) is considered. \(U_R\) is a functor in the category \textit{Tych}. It is proved that \(U_R\) has all properties of a normal functor, with the exception of point preservation. The topic looks very sophisticated. It would be nice to have an application of the results, say, in the theory of stochastic processes.