Finite sums of ridge functions on convex subsets of R^n

We prove that each function of one variable forming a continuous finite sum of ridge functions

on a convex body belongs to the VMO space on every compact interval of its domain. Also, we prove that for the existence of finite limits of the functions of one variable forming the sum at the 

corresponding boundary points of their domains, it suffices to assume the Dini condition on the 

modulus of continuity of some continuous sum of ridge functions on a convex body E at some boundary point. Further, we prove that the obtained (Dini) condition is sharp.