DefinitionDefinition: Literature-sourcedProof: Not applicablejudge 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.

Sigma-algebras

Definition

Let $X$ be a set. A sigma-algebra on $X$ is an algebra of subsets $A$ (Algebras of subsets) that is closed under countable unions: whenever $(A_{n})_{n \in N}$ is a sequence in $A$ ,

$⋃_{n \in N} A_{n} \in A .$

The pair $(X, A)$ then has a fixed ambient set $X$ . Complements in the sigma-algebra axioms always mean complements relative to that $X$ .

Sigma-algebras

Definition

Definition references

Depends on

Dependency tree · 1 level

Sources