DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

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.

Regular complex Borel measures

Definition

Let $X$ be a locally compact Hausdorff space. A complex Borel measure $μ$ on $X$ is regular if its total variation $∣ μ ∣$ is a regular Borel measure in the preceding, all-Borel sense. This total-variation convention is the one that controls $∣ \int f d μ ∣$ and the norm in the $C_{0}$ representation theorem.

Depends on

Dependency tree · 2 levels

Sources

Donald L. Cohn, Measure Theory, 2nd ed., Proposition 7.3.4