2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70773A strongly special subvariety of a Shimura variety $S$ is (essentially) a subvariety associated to a semi-simple sub-Shimura datum. We prove that the set of probability measures canonically associated to to strongly special subvarieties is compact. More precisely: If $μ_n$ is a sequence of such probability measures associated to strongly special subvarieties $Z_n$ of $S$ there exists a subsequence $μ_{n_k}$ which converge to a measure $μ_Z$ canonically associated to a strongly special subvariety $Z$ and for all $k>>0$ $Z_{n_k}$ is contained in $Z$. We give some application to the Andre-Oort conjecture: If $X$ is a subvariety of $S$ then there exists at most finitely many maximal (amongs subvarieties of $X$) strongly special subvarieties of $X$ as predicted by the Andre-Oort Conjecture. The proof uses Ratner's theory, some results of Mozes-Shah and Dani-Margulis.Latex, French, 20. pages, no figure. to appear in Annals of MathAlgebraic GeometryNumber Theorytext