factor is called a Sudakov form factor, and it is, in this case, given by $$S(q_{\perp ,i}^2 ,q_{\perp ,i-1}^2 )=exp\biggl[-\int_{q_{\perp ,i-1}^2}^{q_{\perp
    ,i}^2} \frac{4 \alpha _s}{3 \pi} \frac{dq_{\perp ,i}^2}{q_{\perp ,i}^2}
    \int_{0}^{1-\epsilon } \frac{dz_i}{1-z_i} \biggr]$$ where the $\epsilon$ is introduced as a cutoff since the integral diverges for $z=1$. Generally, if we have an ordering in a variable $t$ and the probability, $P(t)$, for something to occur at a certain $t$ value, the Sudakov form factor is given by $$S(t_1 ,t_2 )=exp\biggl[-\int_{t_1}^{t_2} dtP(t) \biggr]$$ Here $(t_1,t_2)$ is the interval where an emission was allowed but did not occur. Summing over the number, $n$, of links in the chain, the following expression for the structure function can be derived (for a quark chain) $$F\sim \sum_{n} \prod_{i=1}^{n} \biggl[ \int \frac{4 \alpha _s}{3
  \pi}  \frac{dq_{\perp ,i}^2}{q_{\perp ,i}^2}  \frac{dz_i}{1-z_i} S(q_{\perp
  ,i}^2 ,q_{\perp ,i-1}^2 ) \theta (q_{\perp ,i} - q_{\perp ,i-1})\biggr] \delta (x -
  \prod_{j}^{n} z_j x_0 ) \theta ( Q^2 - q_{\perp, n}^2) 
\label{eq:dglap}$$

Subleading corrections in ln$1/x$ are taken into account by replacing the $1/(1-z_i)$ term by the full splitting function, $P(z)$. Including spin effects gives $$\frac{1}{1-z} \longrightarrow \frac{1}{2} \frac{1+z^2}{1-z}$$ By taking the derivative of eq.  with respect to ln$Q^2$ we obtain the DGLAP (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi) 