Lean verification record
Checked Artifact: Monotone Convergence Theorem (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.lintegral_iSup- Module
Mathlib.MeasureTheory.Integral.Lebesgue.Add- Source file checked
Mathlib/MeasureTheory/Integral/Lebesgue/Add.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 monotone convergence theorem for a natural-number-indexed sequence f : ℕ → α → ℝ≥0∞ whose terms are measurable and which is monotone in the pointwise function order. It concludes that the lintegral of the pointwise supremum equals the supremum of the lintegrals. Nonnegativity is encoded by ℝ≥0∞, so no integrability or finiteness hypothesis is required and either side may be ∞. The selected declaration does not state the nearby almost-everywhere-measurable/almost-everywhere-monotone variant, a signed or Bochner-integral theorem, convergence for a nonmonotone sequence, or a quantitative rate.
This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.