Most of this was cited from https://www.ippp.dur.ac.uk/~krauss/Lectures/QuarksLeptons/QCD/DGLAP_2.html. I'm just wondering if someone could explain where equations (1)-(4) come from? I think (3) is clear from the definition of the plus distribution but I am not sure how (4) comes from the earlier equations and how (1) and (2) are initially obtained.

Thanks!