Math and science::Analysis::Tao, measure::02. Lebesgue measure

Outer Lebesgue measure of countable union of almost disjoint boxes

If a set is expressible as a countable union of almost disjoint boxes, then what is it's outer Lebesgue measure?

Let $E = ⋃_{n = 1}^{\infty} B_{n}$ be a countable union of almost disjoint boxes. Then

[

m^{*} (E) = ?

]

What else equals the RHS above? We can say the following:

For a countable union of disjoint boxes, the Lebesgue outer measure is equal to the Jordan inner measure.

01.09.2020