A D11: Set $\Lambda \subseteq \mathcal{P}(X)$ is a Lambda algebra on $X$ if and only if
(1) | \begin{equation} X \in \Lambda \end{equation} |
(2) | \begin{equation} \forall \, E, F \in \Lambda \left( E \subseteq F \quad \implies \quad F \setminus E \in \Lambda \right) \end{equation} |
(3) | \begin{equation} \forall \, E_0, E_1, E_2, \dots \in \Lambda \left( E_0 \subseteq E_1 \subseteq E_2 \subseteq \dots \quad \implies \quad \bigcup_{n \in \mathbb{N}} E_n \in \Lambda \right) \end{equation} |