  We show how the mass function of dense cores (CMF) which results from the
gravoturbulent fragmentation of a molecular cloud evolves in time under the
effect of gas accretion. Accretion onto the cores leads to the formation of
larger numbers of massive cores and to a flattening of the CMF. This effect
should be visible in the CMF of star forming regions that are massive enough to
contain high mass cores and when comparing the CMF of cores in and off dense
filaments which have different environmental gas densities.
