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real analysis - Counterexample to $m(B\setminus A) = m(B) - m(A)$ - Mathematics

I just proved the following theorem for my measure theory course (note that $m$ is the Lebesgue measure on $\mathbb{R}$) Prove that if $A \subset B$ and $m(A)$ is finite, then $m(B\setminus A) = m...

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real analysis - Is there a simple example such that $A\cap B=\emptyset, m^*(A\cu

Is there a simple example such that $A\cap B=\emptyset, m^*(A\cup B)<m^*A+m^*B$? Here $m^*$ is the Lebesgue outer measure on $\Bbb R$. Of course, we can show the existence by contradition, and ...

For a complex measure m, why is m(B = E - A) = m(E) - m(A)? - Mathematics Stack

So, this should be a little obvious, but not to me at the moment. Why is $m(B = E - A) = m(E) - m(A)$? Of course, all given sets are measurable. Thanks.