π-system

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(set theory, measure theory, probability theory) A non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.

このボタンはなに？

To apply Dynkin's lemma, first verify that the family of measurable sets forms a π-system.

詳細

意味（1）

(set theory, measure theory, probability theory) A non-empty collection of subsets of a given set Ώ that is closed under non-empty finite intersections.

To see this, first check that 𝜎(X_0,X_1,…)=𝜎(ℱ_0), where ℱ_0:=∪ ᪲ₖ₌₀𝜎(X_0,…,X_k) is a field and, in particular, a boldsymbol 𝜋-system.

詳細

π-systems （ 複数形 ）