# Where can I find the proofs of these measure theory Propositions?

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) :

1. 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

2. Every unbounded Interval$\subset \mathbb{R}^n$ is measurable with $m(I) = \infty$ and $\mathbb{R}^n$ is measurable with $m(\mathbb{R}^n) = \infty$

3. Every open Subset $G\subset \mathbb{R}^n$ is measurable.

4. Every closed subset of $\mathbb{R}^n$ is measurable

5. 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.