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.
Chart surface measure and Hausdorff measure: a boundary of scope
Discussion
The definition Unnormalised Hausdorff measure provides a metric notion of size, and Euclidean Hausdorff measure is proportional to Lebesgue measure relates its ambient-dimensional instance to Euclidean volume. The planned PDE applications may use chartwise change of variables already supplied by the integration track. Identifying chart-defined hypersurface measure with an appropriately normalised Hausdorff measure requires a further geometric-measure theorem. That identification belongs to a future treatment; it is not established or used here. Fremlin separates these topics between §§264 and 265.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
11 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
- Fremlin chapter 26 introduction and 265A opening; design geometric-measure receipt (standard reference, not scraped)