Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17
How statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Algebras of subsets
Definition
Let be a set. An algebra of subsets of is a family such that:
- ;
- if , then ;
- if , then .
Thus an algebra is closed under complements relative to its fixed ambient set, finite unions, finite intersections, and differences. In particular belongs to every algebra on .
Used by
- Sigma-algebras Definition
- FALSE: every monotone class is an algebra False statement
- An algebra closed under countable disjoint unions is a sigma-algebra Lemma
- An algebra closed under increasing countable unions is a sigma-algebra Lemma
- Every member of the generated monotone class intersects every original algebra member inside the generated class Lemma
- The monotone class generated by an algebra is closed under complements Lemma
Dependency tree · next 3 levels
Nothing. This result depends on no other item in the library.
Sources
- R. F. Bass, Real Analysis for Graduate Students, version 5.0, Definition 2.1 (standard reference, not scraped)