Dear all,

For any sigma-finite measure $\mu$ on the Borel subsets of a metric space X (separable if needed), we recall that a $\mu$-continuity set is any Borel set B such that $\mu(boundary of B) = 0$

I would like to find a good reference (book or article) where is treated clearly the proof of the result which establishes that the sigma-algebra generated by the $\mu$-continuity sets is equal to the Borel sigma-algebra.

Sincerely,

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