  We prove a uniform boundary Harnack inequality for nonnegative harmonic
functions of the fractional Laplacian on arbitrary open set $D$. This yields a
unique representation of such functions as integrals against measures on
$D^c\cup \{\infty\}$ satisfying an integrability condition. The corresponding
Martin boundary of $D$ is a subset of the Euclidean boundary determined by an
integral test.
