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Posted

Prove or disprove:

If the boundary of set omega in R^d has an outer measure zero, then omega is Lebesgue measurable.

I was trying to come up with a counter example, but I couldn't. Then I tried

to prove it, yet I was not able to do so. Please help me :-(

Posted

Just to let you know that I'm thinking about the problem. It sort of makes sense and I'm unable to find a counter-example, so it's beginning to look true. Did you get anywhere with this?

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