Sampling interval $T$ as a multiplier in digital processing of a continuous-time signals
I don't think it's a typo, but it has to do with the sampling process. As shown in Eq. $(4.30)$ in the 3rd edition of Discrete-time Signal Processing by Oppenheim and Schafer, (ideal) sampling involves scaling by $1/T$, where $T$ is the sampling period. If the continuous-time signal $x_c(t)$ is ideally band-limited, the spectrum of the discrete-time signal $x_d[n]=x_c(nT)$ after sampling is given by
$$X(e^{j\Omega T})=\frac{1}{T}X_c(j\Omega)\tag{1}$$
So if you divide both sides of Eq. $(155)$ by $T$ you see that on the right-hand side you get the scaled spectrum of the continuous-time signal, which equals the spectrum of the discrete-time signal.