Let $T$ be a countable set, $\mathcal{A}=\{A\subseteq T:A\text{is finite or}{A}^{c}\text{is finite}\}$ and $\mu :\mathcal{A}\to [0,\mathrm{\infty})$ definided for every $A\in \mathcal{A}$ by

$\mu (A)=\{\begin{array}{ll}0,& \text{if}A\text{is finite}\\ 1,& \text{if}{A}^{c}\text{is finite.}\end{array}$

Then every set $A\in \mathcal{A}$, such that ${A}^{c}$ is finite, is an atom with respect of $\mu $.

But I can't see how it is concluded that every set $A\in \mathcal{A}$, such that ${A}^{c}$ is finite, is an atom with respect of $\mu $, can someone help me?

$\mu (A)=\{\begin{array}{ll}0,& \text{if}A\text{is finite}\\ 1,& \text{if}{A}^{c}\text{is finite.}\end{array}$

Then every set $A\in \mathcal{A}$, such that ${A}^{c}$ is finite, is an atom with respect of $\mu $.

But I can't see how it is concluded that every set $A\in \mathcal{A}$, such that ${A}^{c}$ is finite, is an atom with respect of $\mu $, can someone help me?