Alphabeta MathHow 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 Borel measure on an LCH space
Definition
A regular Borel measure here is a Radon measure for which every Borel satisfies , with equality allowed at . Thus regularity strengthens the preceding open-set formula; it is not being used as a synonym for Radon.
Depends on
Used by
- Regular complex Borel measures Definition
- Every finite Borel measure on a compact Hausdorff space is regular False statement
- Inner regularity on open sets implies inner regularity on all Borel sets False statement
- Positive C₀(X) functionals have finite regular representing measures Lemma
- Lusin's theorem for a Radon measure Theorem
- Sigma-compact open sets make locally finite Borel measures regular Theorem
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
- Donald L. Cohn, Measure Theory, 2nd ed., §7.3 (standard reference, not scraped)