  It is known that the class $\mathcal{U}_{\beta}$, of generalized
s-selfdecom-posable probability distributions, can be viewed as an image via
random integral mapping $\mathcal{J}^{\beta}$ of the class $ID$ of all
infinitely divisible measures. We prove that a composition of the mappings
$\mathcal{J}^{\beta_1}, \mathcal{J}^{\beta_2}, ..., \mathcal{J}^{\beta_n}$ is
again random integral mapping but with a new inner time. In a proof some form
of Lagrange interpolation formula is needed. Moreover, some elementary formulas
concerning the distributions of products of powers of independent uniformly
distributed random variables as established as well.
