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Question is to show that $S(I_{d})=B_{R} \cap [0,1]$, where $I_{d}$ denote the class of all subintervals of $[0,1]$ with dyadic endpoints and $B_{R}$ is sigma algebra of borel subsets of $R$. I have no idea to proceed with this. Any hint please.

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If $U$ is open and $x \in U$ then there is a dyadic interval $I_d$ such that $x \in I_d \subset U$. From this conclude that $U$ is a (countable) union of dyadic intervals. Can you complete the argument now?.

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  • $\begingroup$ Sorry sir, I didn't get it $\endgroup$ – Believer Mar 15 at 17:25

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