Why is it called continuous-time frequency? I'm just wondering about the CTFT. My lecturer refers to capital Omega $\Omega$ in the following as being the continuous-time frequency:



Why is it called continuous-time frequency here but in the DTFT the small omega is called discrete-time frequency? CTFT and DTFT both give continuous signals out.
$\Omega$ is the usual angular frequency in radians per second, and is equal to $2 \pi f$. It is the way to measure frequency for continuous-time signals.

In discrete-time, frequency is measured in radians per sample, and is denoted as $\omega$. Here, a frequency component with $\omega = 2\pi$ is indistinguishable from $\omega = 0$.

$\Omega$ and $\omega$ is the notation in texts such as Oppenheim-Schafer. Other authors use $\theta$ for discrete-time, and the classic $\omega$ for continuous-time signals.