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 class $L^{1} (μ)$ of integrable functions

Definition

For a measure $μ$ , write $L^{1} (μ) : = {f : X \to C : f is integrable} .$ Here integrable is the notion introduced in Integrable real and complex functions, and their integrals.

On this page $L^{1} (μ)$ is the class of integrable representatives. The later Banach-space page will pass to almost-everywhere equivalence classes.

Depends on

Integrable real and complex functions, and their integrals

Dependency tree · 2 levels

Sources

Gerald B. Folland, Real Analysis, 2nd ed., §2.3