  In this article we study the isotropy stratification of a linear
representation $V$ of a compact Lie group $G$. We prove that the closed
isotropy strata are real algebraic manifolds and that for each isotropy
subgroup $H$, every rational invariant of the induced representation
$(V^{H},N(H))$ can be obtained as the restriction of a global invariant of
$(V,G)$, where $N(H)$ is the normalizer of $H$ and $V^{H}$ is the fixed point
set of $H$.
