We consider r.v. x₁,x₂,Ybeing independent fboth of F₁,F₂,FF_Y. We assume that   . It is well known that under such circumstances F₁and F₂do not necessarily coincide, even if τ=∞ But with appropriate additional assumptions we obtain at least F(x) = F₂(x)j x≤τ or even F₁=F₂. Assumptions on F_Yare either lext (F_Y)=0 or lext (F_Y) =-∞. In the latter case the desired result F₁‵F₂follows if .

This way new light is shed on the“Khesttchine phenomenon”, see [5]. The recent continuation theory of d.f. plays a considerable role, but, nioreover, the theory of Phbagmn-lindelf is applied to a large extent.