# How to prove that cuboids are Lebesgue measurable?

• A
Hello,
how do I have to start to prove that cuboids are measurable in the context of the Lebesgue measure?
Best wishes
Maxi

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mathman
Measure theory starts from the definition of measure of an interval is equal to its length. A cuboid is just the 3d analog of an interval. You can start with measure equals volume or you can define 3 space as the direct product of 3 lines and go on from there.

martinbn
Measure theory starts from the definition of measure of an interval is equal to its length. A cuboid is just the 3d analog of an interval. You can start with measure equals volume or you can define 3 space as the direct product of 3 lines and go on from there.
I think the subtlety comes when the cuboid is rotated.

mathman
The coordinate system can be rotated with it.

martinbn