Properties of the Liouville measure

Question

Could someone point me to references where general properties of the Liouville measure, $\mu_L$, would be explicitly discussed?

Questions:

1. Can $\mu_L$, as usually defined, always be viewed as a measure in the standard sense of measure theory?

2. If so, what is the underlying $\sigma$-algebra? And does it contain all singletons? Is $\mu_L$ always a $\sigma$-finite measure?

3. Does $\mu_L$ always enjoy some nice continuity properties? Is it e.g. always continuous from above/from below?

4. Is it guaranteed that $\mu_L$ has no point masses?

5. Is $\mu_L$ a probability measure on any energy surface?

Thoughts: I've seen geometric definitions of Liouville measure (e.g. Two different definitions of a Liouville measure). I don't know whether it's obvious that they settle some/all of the above questions.