These propositions are listed as examples in my script and I want to know the proofs (I am not able to prove them myself, unfortunately, because im not smart and very new to measure theory) :
If $I=I_{1}\times ... I_n$ is a bounded Interval on $\mathbb{R}^n$, then I is measurable and it holds that $m(I)=|I_{1}|...|I_n|$ (m(I) is called the elementary n-dimensional volume
Every unbounded Interval$\subset \mathbb{R}^n$ is measurable with $m(I) = \infty$ and $\mathbb{R}^n$ is measurable with $m(\mathbb{R}^n) = \infty$
Every open Subset $G\subset \mathbb{R}^n$ is measurable.
Every closed subset of $\mathbb{R}^n$ is measurable
Every compact Subset of $\mathbb{R}^n$ has a finite measure
Do you know of a source where I can find proofs to these examples or what I have to search for to find them.
Thx in advance
