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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.