DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-27

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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

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Gerald B. Folland, Real Analysis, 2nd ed., §2.3 (standard reference, not scraped)

The class L1(μ)L1(μ) of integrable functions