Technical Lean evidence record
Checked Artifact: Radon–Nikodym Theorem (mathlib)
Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.
ProofAtlas record
What has been checked
These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.
Mechanical evidence
- Declaration checked
MeasureTheory.Measure.absolutelyContinuous_iff_withDensity_rnDeriv_eq- Module
Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym- Source file checked
Mathlib/MeasureTheory/Measure/Decomposition/RadonNikodym.lean- Package commit
5e932f97dd25535344f80f9dd8da3aab83df0fe6- Build
- passed · transcript retained
- Unfinished proof steps
- None found by the recorded no-sorry scan
- Axiom closure
- Classical.choice, Quot.sound, propext
- Clean collection provenance
- Recorded
Evidence boundary
This page indexes Mathlib's positive-measure Radon–Nikodym theorem. For measures μ and ν on one measurable space, it assumes HaveLebesgueDecomposition μ ν and states the exact equivalence μ ≪ ν ↔ ν.withDensity (rnDeriv μ ν) = μ. The density is ENNReal-valued. The selected declaration is not the signed-measure theorem, not a vector-measure theorem, and not an assumption-free existence claim for arbitrary measure pairs.
This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.