  Let $X$ be a compact metric space and let $\Lambda$ be a $\Z^k$ ($k\ge 1$)
action on $X.$ We give a solution to a version of Voiculescu's problem of
AF-embedding: The crossed product $C(X)\rtimes_{\Lambda}\Z^k$ can be embedded
into a unital simple AF-algebra if and only if $X$ admits a strictly positive
$\Lambda$-invariant Borel probability measure.
  Let $C$ be a unital AH-algebra, let $G$ be a finitely generated abelian group
and let $\Lambda: G\to Aut(C)$ be a monomorphism. We show that
$C\rtimes_{\Lambda} G$ can be embedded into a unital simple AF-algebra if and
only if $C$ admits a faithful $\Lambda$-invariant tracial state.
