  Properties of eigenstates of one-particle Quantum Hall Hamiltonians localized
near the boundary of a two-dimensional electron gas - so-called edge states -
are studied. For finite samples it is shown that edge states with energy in an
appropriate range between Landau levels remain extended along the boundary in
the presence of a small amount of disorder, in the sense that they carry a
non-zero chiral edge current. For a two-dimensional electron gas confined to a
half-plane, the Mourre theory of positive commutators is applied to prove
absolute continuity of the energy spectrum well in between Landau levels,
corresponding to edge states.
