  We prove a compactness theorem for embedded measured hyperbolic Riemann
surface laminations in a compact almost complex manifold $(X, J)$. To prove
compactness result, we show that there is a suitable topology on the space of
measured Riemann surface laminations induced by Levy-Prokhorov metric. As an
application of the compactness theorem, we show that given a biholomorphism of
$\phi $ of a closed complex manifold $X$, some power $\phi^k $ ($k>0$) fixes a
measured Riemann surface lamination in $X$.
