I couldn't understand the monotone class theorem because of this lemma: "Every $\sigma$ algebra is a monotone class."
How i can prove it?
2026-02-22 20:57:05.1771793825
every $\sigma$ algebra is a monotone class
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A $\sigma$-algebra is closed under countable union and countable intersection, so in particular under increasing countable union and decreasing countable intersection.