generated from smyalygames/quartz
502 B
502 B
Definition
A $\sigma$-algebra in a set X is a collection of subsets, so called measurable sets, of X such that (the requirements are):
X \in MA \in M \implies A^{\complement} \in M(A^{\complement} \equiv X \setminus A) (X^{\complement} = \emptyset \in M)A_{n} \in M \implies \cup^{\infty}_{n=1} A_{n} \in M(\implies \cap^{\infty}_{n=1} A_{n} = (\cup^{\infty}_{n=1}A^{\complement})^{\complement} \in M))