  The mean field limit with time dependent weights for a 1D singular case,
given by the attractive Coulomb interactions, is considered. This extends
recent results [1,8] for the case of regular interactions. The approach taken
here is based on transferring the kinetic target equation to a Burgers-type
equation through the distribution function of the measures. The analysis
leading to the stability estimates of the latter equation makes use of Kruzkov
entropy type estimates adapted to deal with nonlocal source terms.
