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$$\mathcal{R} = \sigma(\mathcal{A})$$

with $\mathcal{A}=\{]a,b]|a,b \in \mathbb{Q}, a < b\}\cup {\emptyset}$

I know that $\mathcal{R}= \sigma(\{]a,b]|-\infty<a\leq b<\infty\})$ so I think $\mathcal{A} \subseteq \mathcal{R}$ and if I can show that $\mathcal{A}$ is a $\pi-$ systeme it follows by the $\pi-\lambda$ theorem that $\sigma(\mathcal{A})\subset \mathcal{R}$.

I could do the reverse implication the same way but then I need to prove that $\{]a,b]|-\infty<a\leq b<\infty\} \subset \sigma(\mathcal{A})$, but I'm struggling with this implication.

Anyone?

Thanks in advance.