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Aug 24, 2023 at 21:20 comment added Fedor Petrov An open set $U$× on the real line is a disjoint union of intervals, which may be defined as inclusion-maximal intervals contained in $U$. Closed segments/intervals are the same, yes.
Aug 24, 2023 at 20:01 comment added Ross Ure Anderson Could you please clarify your informal definition of a measure : $\mu(A) = $ 'the sum of lengths of the inclusion-maximal intervals' of $A$ - I am not clear what 'inclusion-maximal interval' means. Also by 'closed segment' do you mean 'closed interval' ?
Aug 24, 2023 at 19:42 history answered Fedor Petrov CC BY-SA 4.0