Reconstituting the distribution of the components of a random Vector from distributions of certain statistics

Let (X₁, ..., X_n) be a random vector with independent components. It is proven in this paper that, under certain restrictions, the distributions of the pairS ₁=sup (a ₁X₁, ..., a_nX_n) andS ₂=sup (b₁X₁,...,b_nX_n) univocally define the distribution function of the components X_j.Translated from Matematicheskie Zametki, Vol. 13, No. 6, pp. 889–892, June, 1973.