Infinitesimal orbit type theorem for normalizable actions

Let α:G×M→M be a differentiable action of a Lie group G on a connected differentiable manifold M. Assume that the local tube theorem holds at every x∈M. Then the following is proved: there is a maximal infinitesimal orbit type, called the principal, such that the union of the orbits belonging to this infinitesimal type is an open and dense set in M.