Theorems · Theorem · measure theory
MeasureTheory.iSup_lintegral_measurable_le_eq_lintegral
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (f : α → ENNReal),
⨆ g, ⨆ (_ : Measurable g), ⨆ (_ : g ≤ f), ∫⁻ (a : α), g a ∂μ = ∫⁻ (a : α), f a ∂μ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.SimpleFuncproof · cited by 411
- le_of_eqproof · cited by 366
- iSup_leproof · cited by 190
- iSup₂_leproof · cited by 96
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_measurable_le_lintegral_eqproof · cited by 8
- MeasureTheory.lintegral_map_leproof · cited by 3
- MeasureTheory.lintegral_withDensity_eq_lintegral_mul_non_measurableproof · cited by 2
- MeasureTheory.lintegral_withDensity_le_lintegral_mulproof · cited by 1