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

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A Borel measure on $R$ that is finite on compact sets

Definition

A Borel measure on $R$ finite on compact sets is a measure

$μ : B (R) \to [0, + \infty]$

on the Borel sigma-algebra The Borel sigma-algebra of a topological space such that

$μ (K) < + \infty for every compact K \subseteq R .$

This is the one-dimensional finiteness hypothesis used throughout the Lebesgue-Stieltjes correspondence on this page.

Depends on

Used by

Dependency tree · two levels

8 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., Section 1.5 (standard reference, not scraped)

A Borel measure on RR that is finite on compact sets