  We provide a general criterion to deduce maximal amenability of von Neumann
subalgebras $L\Lambda \subset L\Gamma$ arising from amenable subgroups
$\Lambda$ of discrete countable groups $\Gamma$. The criterion is expressed in
terms of $\Lambda$-invariant measures on some compact $\Gamma$-space. The
strategy of proof is different from S. Popa's approach to maximal amenability
via central sequences [Po83], and relies on elementary computations in a
crossed-product C*-algebra.
