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Incoming links: Atom (measure theory)
Atom of a sigma-algebra Created 2026-09-24 Updated 2026-10-14
A sigma-algebra atom is set-theoretically minimal. An atom is instead indivisible only modulo sets of measure zero.
An atom of a sigma-algebra is a nonempty measurable set containing no proper nonempty measurable subset. A finite sigma-algebra partitions its underlying set into atoms, and each measurable set is a union of them.