Lean verification record
Checked Artifact: Change of Variables Formula (mathlib)
Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.
Verification result
The recorded Lean checks passed
- Build replaypassed with retained transcript
- Unfinished stepsNone found
- Source identityPinned commit and file recorded
- Dependency profileAxiom closure recorded
Reproducibility details
What the checker recorded
- Declaration checked
MeasureTheory.integral_image_eq_integral_abs_det_fderiv_smul- Module
Mathlib.MeasureTheory.Function.Jacobian- Source file checked
Mathlib/MeasureTheory/Function/Jacobian.lean- Package commit
5e932f97dd25535344f80f9dd8da3aab83df0fe6- Build transcript
- passed · retained with this record
- Unfinished proof steps
- None found by the recorded no-sorry scan
- Axiom closure
- Classical.choice, Quot.sound, propext
- Collection provenance
- Clean source state recorded
ProofAtlas record
What has been checked
Mathlib is the source of the theorem; the local Lean replay and page review are separate.
Evidence boundary
Exact formal statement only
This page indexes Mathlib's finite-dimensional Bochner-integral change-of-variables declaration for a measurable set s and a map f that is injective and differentiable within s with recorded derivative f'. The endpoint is exactly the equality between the integral of an F-valued function g on f '' s and the source integral weighted by the absolute determinant of f'. It does not assume or conclude a global diffeomorphism, global injectivity or surjectivity, an open domain, a continuously differentiable map, or an everywhere-invertible derivative. The formal declaration quantifies over g : E → F without a separate measurability or integrability hypothesis; its exact Mathlib set-integral semantics remain authoritative.
This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.