Let $(X,\Sigma,\mu)$ be a finite measure space. Call $\mu$ nonatomic if for any $A\in\Sigma$ with $\mu(A)>0$ there exists $B\in\Sigma$ with $B\subset A$ and $0<\mu(B)<\mu(A)$. 

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> Suppose that $\mathcal S$ be the algebra that generates $\Sigma$. I am asking to what is the relation between nonatomicity of $\mu$ and $\mu|\_\mathcal S$.
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