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.
To use Fubini safely, first use Tonelli on |f|
The safe workflow is:
- apply Tonelli's theorem for nonnegative measurable functions on a sigma-finite product to ;
- check that the resulting iterated integral is finite; then
- invoke Fubini's theorem for L^1 functions on a sigma-finite product.
This is the point of the absolute-integrability hypothesis in Fubini's theorem. Without it, the iterated integrals may exist separately and still disagree.
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
- Gerald B. Folland, Real Analysis, 2nd ed., remark after Theorem 2.37 (standard reference, not scraped)
- John K. Hunter, Measure Theory, Theorem 5.18 (standard reference, not scraped)