  Let $\K$ be a galois CM extension of $\Q$ and $\K_{\infty}$ its cyclotomic
$\Z_p$-extension. Let $A_n$ be the $p$-parts of the class groups in the
intermediate subfields $\K_n \subset \K_{\infty}$ and $\rg{A} = \varprojlim_n
A_n$. We show that the $p$-rank of $\rg{A}$ is finite, which is equivalent to
the vanishing of Iwasawa's constant $\mu$ for $\rg{A}$. (Currently withdrawn)
