  It is anticipated that hard double parton scatterings will occur frequently
in the collisions of the LHC, producing interesting signals and significant
backgrounds to certain single scattering processes. For double scattering
processes in which the same hard scale t = ln(Q^2) is involved in both
collisions, we require the double parton distributions (dPDFs)
D_h^{j_1j_2}(x_1,x_2;t) in order to make theoretical predictions of their rates
and properties. We describe the development of a new set of leading order dPDFs
that represents an improvement on approaches used previously. First, we derive
momentum and number sum rules that the dPDFs must satisfy. The fact that these
must be obeyed at any scale is used to construct improved dPDFs at the input
scale Q_0, for a particular choice of input scale (Q_0^2 = 1 GeV^2) and
corresponding single PDFs (the MSTW2008LO set). We then describe a novel
program which uses a direct x-space method to numerically integrate the LO
DGLAP equation for the dPDFs, and which may be used to evolve the input dPDFs
to any other scale. This program has been used along with the improved input
dPDFs to produce a set of publicly available dPDF grids covering the ranges
10^{-6}<x_1<1, 10^{-6}<x_2<1, and 1<Q^2<10^9 GeV^2.
