that $p_\perp'\geqslant p_\perp$ and $p_+'\leqslant p_+$. Therefore the rapidity will always increase due to a recoil. There is however a problem with this; as we order the emissions in rapidity the last emitted gluon will always have the largest rapidity, and we would like it to remain so. Since the rapidity of the emitters increase due to recoil, there is the possibility that one of the emitters, or both of them, after the recoil ends up with a rapidity larger than the rapidity of the emitted gluon. The next time we emit a gluon, the rapidity of that emitter would then determine the region in which the new emission can occur, in a sense violating the ordering we had. To prevent this we require that $y_i',y_j'\leqslant y_n$; if this constraint is not satisfied a new gluon is generated. Without this constraint there would also be a lot of gluons in the final state which have rapidities larger than the maximum rapidity, due to the recoils.

Upper Bound for the Dipole Size
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The $p_+$ conservation, as we mentioned, will give a cutoff for small dipoles, limiting the number of small dipoles. We can, however, also get extremely large dipoles, especially 