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.
Lambda-systems, or Dynkin systems
Definition
Let be a set. A lambda-system, or Dynkin system, on is a family such that:
- ;
- if and , then ;
- if and every , then .
Used by
- The lambda-system generated by a family of sets Definition
- FALSE: every lambda-system is closed under finite intersections False statement
- A lambda-system closed under finite intersections is a sigma-algebra Lemma
- For a member A of a lambda-system D, the sets B with A intersection B in D form a lambda-system Lemma
- A family is a lambda-system exactly when it contains X and is closed under complements and countable disjoint unions Proposition
- Every sigma-algebra is a lambda-system and a monotone class Proposition
Dependency tree · next 3 levels
Nothing. This result depends on no other item in the library.
Sources
- A. Dembo, Probability Theory lecture notes, Definition 1.1.36 (standard reference, not scraped)