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(Q2) is involved in both collisions, we require the double parton distributions (dPDFs) Dj1j2 h (x1, x2; 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 Q0, for a particular choice of input scale (Q20 = 1 GeV2) 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 < x1 < 1, 10−6 < x2 < 1, and 1 < Q2 < 109 GeV2.