The radiance L(p, w) is a scalar not a vector, right?

I believe so. However, what does it mean for flux $\Phi$ to take in $p$ and $\omega$? I thought flux was defined per point; how does $\omega$ affect this definition?

The nit can be thought of as a unit of brightness - for example, a laptop screen might have a peak brightness of 500 nits. More info