  We have measured circularly polarized photoluminescence in monolayer MoSe2
under perpendicular magnetic fields up to 10 T. At low doping densities, the
neutral and charged excitons shift linearly with field strength at a rate of
$\mp$ 0.12 meV/T for emission arising, respectively, from the K and K' valleys.
The opposite sign for emission from different valleys demonstrates lifting of
the valley degeneracy. The magnitude of the Zeeman shift agrees with predicted
magnetic moments for carriers in the conduction and valence bands. The relative
intensity of neutral and charged exciton emission is modified by the magnetic
field, reflecting the creation of field-induced valley polarization. At high
doping levels, the Zeeman shift of the charged exciton increases to $\mp$ 0.18
meV/T. This enhancement is attributed to many-body effects on the binding
energy of the charged excitons.
