Intuition about absolute Continuity/Singularity of measures

Intuition about absolute Continuity/Singularity of measures

Let $\mu$, $\nu$ be two measures, $X= d\nu/d\mu$ their Radon-Nikodym
derivative (in general a random variable). I want to gain an intuition
about the following statements:
$$\int X\; d\mu = 1 \Leftrightarrow \nu << \mu \Leftrightarrow X < \infty,
\nu-a.s.$$ and $$X=0, \mu-a.s. \Leftrightarrow \nu \perp \mu
\Leftrightarrow X = \infty, \nu-a.s.$$
Can someone explain to me what absolute continuity/singularity implies for
their Radon-Nikodym derivative?