(i) | $\mathcal{P}(X)$ is the D80: Power set of $X$ |

**sigma-algebra**on $X$ if and only if

(1) | \begin{equation} \emptyset \in \mathcal{F} \end{equation} |

(2) | \begin{equation} \forall \, E \in \mathcal{F} : X \setminus E \in \mathcal{F} \end{equation} |

(3) | \begin{equation} \forall \, E_0, E_1, E_2, \dots \in \mathcal{F} : \bigcup_{n \in \mathbb{N}} E_n \in \mathcal{F} \end{equation} |