Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17
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.
Measurable spaces and measurable sets
Definition
A measurable space is a pair consisting of a set and a sigma-algebra on (Sigma-algebras). The members of are the measurable subsets of .
Depends on
Used by
- A measurable function between measurable spaces Definition
- Coordinate maps, finite-coordinate cylinders, and the cylinder σ-algebra Definition
- Integral of a simple function against a pvm Definition
- Measurable rectangles in a product of measurable spaces Definition
- Projection valued measure Definition
- Standard Borel spaces Definition
- Newton shell theorem from harmonic mean values Example
- Measurability is relative to sigma-algebras on both domain and codomain Remark
Dependency tree · two levels
2 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
- R. F. Bass, Real Analysis for Graduate Students, version 5.0, Definition 2.1 (standard reference, not scraped)
- T. Tao, An Introduction to Measure Theory, Definition 1.4.12 (standard reference, not scraped)