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.
The separate measurable extension of density integration
Scope
The integration theory on this page is for compactly supported smooth densities, using Riemann integrals in positive-dimensional charts. General measurable nonnegative densities, densities, and associated Radon measures are outside the present construction. Those extensions belong to the separate Lebesgue change-of-variables and regular-measure development. No measurable integration or Radon-representation theorem is asserted or used here.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
7 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
- Nicolaescu Proposition 3.4.3(c), p.113 (standard reference, not scraped)