Singularities of pairs via jet schemes

Let X X be a smooth variety and Y ⊂ X Y⊂ X a closed subscheme. We use motivic integration on the space of arcs of X X to characterize the fact that ( X , Y ) (X,Y) is log canonical or log terminal using the dimension of the jet schemes of Y Y . This gives a formula for the log canonical threshold of ( X , Y ) (X,Y) , which we use to prove a result of Demailly and Kollár on the semicontinuity of log canonical thresholds.