We interpret as determined probability moments some sequences of combinatorial integers and most of the time we can explicit the underlying probability measure . Key words: Moments problems, Generalized and ordinary Bell numbers, Bessel numbers, Subordinators, Exponential functionals, Carleman criterion. 1

Abstract. Let Bn p = {(xi) ∈ Rn; ∑n 1 |xi | p ≤ 1} and let E be a k-dimensional subspace of Rn. We prove that |E ∩ Bn p | 1/k k ≥ |Bn p | 1/n n, for 1 ≤ k ≤ (n − 1)/2 and k = n − 1 whenever 1 < p < 2. We also consider 0 < p < 1 and other related cases. We obtain sharp inequalities involving Gamma function in order to get these results.

Abstract. In the present paper, we give two new proofs for the necessary and sufficient condition α ≤ 1 such that the function x α [lnx − ψ(x)] is completely monotonic on (0, ∞). 1.