## PIERROTS THEORE M FOR SINGULAR RIEMANIAN FOLIATIONS

Riemannian foliations), cf. [3] and [4] . Assume that the manifold M is compact and connected (or the metric is complete) . Then the closure of any leaf is a submanifold. Let k be any number between o and n. Define Ek ={xEM :xEdimL, = k}. The leaves of,1 is Ek are of the same dimension, however they can have holonomy. P. Molino demonstrated ...