Technical Lean evidence record
Checked Artifact: Monotone Convergence 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.lintegral_iSup- Module
Mathlib.MeasureTheory.Integral.Lebesgue.Add- Source file checked
Mathlib/MeasureTheory/Integral/Lebesgue/Add.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 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 is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.