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Artikel ieu keur dikeureuyeuh, ditarjamahkeun tina basa Inggris. Bantuanna didagoan pikeun narjamahkeun. |
Dina matematika, aljabar σ (atawa widang σ) X pikeun sasét S hartina anggota subsét S nu katutup ku sét operasi-operasi nu bisa diitung; aljabar σ utamana dipaké pikeun nangtukeun ukuran S. Ieu konsép penting dina analisis matematika jeung téori probabilitas.
Sacara formal, X kaasup aljabar σ mun jeung ukur mun (jika dan hanya jika, if and only if) miboga pasipatan di handap ieu:
- The empty set is in X,
- If E is in X then so is the complement of E.
- If E1, E2, E3, ... is a sequence in X then their (countable) union is also in X.
From 1 and 2 it follows that S is in X; from 2 and 3 it follows that the σ-algebra is also closed under countable intersections (via De Morgan's laws).
An ordered pair (S, X), where S is a set and X is a σ-algebra over S, is called a méasurable space.