DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + claude-opus-5[1m])audited 2026-08-24

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.

Carathéodory measurable sets

Definition

Let $μ^{*}$ be an outer measure on $X$ (Outer measures). A set $E \subseteq X$ is Carathéodory measurable for $μ^{*}$ when $μ^{*} (A) = μ^{*} (A \cap E) + μ^{*} (A ∖ E)$ for every $A \subseteq X$ .

Write $M_{μ^{*}}$ for the family of all Carathéodory measurable subsets of $X$ . The quantifier over every test set $A$ is part of the definition.

Depends on

Outer measures

Carathéodory measurable sets

Definition

Depends on

Dependency tree · 2 levels

Sources