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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.
