Abstract : In this paper we prove that M p Λ is almost isometric to p in the canonical way when Λ is lacunary with a large ratio. On the other hand, our approach can be used to study also the Carleson measures for Müntz spaces M p Λ when Λ is lacunary. We give some necessary and some sufficient conditions to ensure that a Carleson embedding is bounded or compact. In the hilbertian case, the membership to Schatten classes is also studied. When Λ behaves like a geometric sequence the results are sharp, and we get some characterizations.