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?

### Outer Lebesgue measure of countable union of almost disjoint boxes

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

[$m^*(E) = \quad ?$]

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.