2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121552In this paper, we give necessary and sufficient conditions for Talagrand's like transportation cost inequalities on the real line. This brings a new wide class of examples of probability measures enjoying a dimension-free concentration of measure property. Another byproduct is the characterization of modified Log-Sobolev inequalities for Log-concave probability measures on R.Probability60E15 26D10text