DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-27

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.

The measure with density $f$ relative to $μ$

Definition

Let $(X, A, μ)$ be a measure space and let $f : X \to [0, + \infty]$ be measurable. The measure with density $f$ relative to $μ$ is the measure $f d μ : A \to [0, + \infty], (f d μ) (A) : = \int_{A} f d μ,$ whose measure property is supplied by The indefinite integral of a nonnegative measurable function is a measure.

Definition references

The indefinite integral of a nonnegative measurable function is a measure

Depends on

The indefinite integral of a nonnegative measurable function is a measure

Dependency tree · 2 levels

Sources