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# Use $\mathbb{P}(\vert \hat{s}_n-s\vert > x)\leq a(n,x)$ and $\mathbb{P}(\vert \hat{s}_n-s_n\vert > x)\leq b(n,x)$ to bound $\vert s_n – s\vert$

Let $$s, s_n\in\mathbb{R}$$ and $$\hat{s}_n$$ be a random variable.

I have two concentration inequalities:

$$\mathbb{P}(\vert \hat{s}_n-s\vert > x)\leq a(n,x)$$ for all $$n\geq1$$ and $$x>0$$;
and
$$\mathbb{P}(\vert \hat{s}_n-s_n\vert > x)\leq b(n,x)$$ for all $$n\geq1$$ and $$x>0$$.

Is there a way to bound $$\vert s_n – s\vert$$?