generated from smyalygames/quartz
8 lines
502 B
Markdown
8 lines
502 B
Markdown
# Definition
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A $\sigma$-algebra in a set $X$ is a collection of subsets, so called measurable sets, of $X$ such that (the requirements are):
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1. $X \in M$
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2. $A \in M \implies A^{\complement} \in M$ ($A^{\complement} \equiv X \setminus A$) ($X^{\complement} = \emptyset \in M$)
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3. $A_{n} \in M \implies \cup^{\infty}_{n=1} A_{n} \in M$ ($\implies \cap^{\infty}_{n=1} A_{n} = (\cup^{\infty}_{n=1}A^{\complement})^{\complement} \in M)$)
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# Related Terminologies/Functions
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- [[Measurable]]
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- [[Measure]] |