  We measure the momentum distribution of a 2D trapped Bose gas and observe the
increase of the range of coherence around the Berezinskii-Kosterlitz-Thouless
(BKT) transition. We quantitatively compare our observed profiles to both a
Hartee-Fock mean-field theory and to quantum Monte-Carlo simulations. In the
normal phase, we already observe a sharpening of the momentum distribution.
This behavior is partially captured in a mean-field approach, in contrast to
the physics of the BKT transition.
