I was wondering how whether this works: Choose $A=\cup_{r \in Q}r+F$ where F denotes the Fat Cantor Set.

To be precise, if μ denotes Lebesgue measure, how would one show that this A as a Borel set A⊂R such that $0<μ(A∩I)<μ(I)$ for every interval I in R?

A is not R by Baire Category theorem. But I haven't made much progress thereafter.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.