Definition 13.2.2 ($\lambda$-System). Let $X$ be a set and $\alg \subset 2^{X}$, then $\alg$ is a $\lambda$-system/$d$-system if:

1. $\emptyset, X \in \alg$.

2. For any $E, F \in \alg$ with $E \subset F$, $F \setminus E \in \alg$.

3. For any $\seq{A_n}\subset \alg$ with $A_{n} \subset A_{n+1}$ for all $n \in \nat^{+}$, $\bigcup_{n \in \nat^+}A_{n} \in \alg$.