Theorems · Theorem · measure theory
MeasureTheory.lintegral_iSup
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : ℕ → α → ENNReal},
(∀ (n : ℕ), Measurable (f n)) → Monotone f → ∫⁻ (a : α), ⨆ n, f n a ∂μ = ⨆ n, ∫⁻ (a : α), f n a ∂μMonotone convergence theorem, version with Measurable functions.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites61
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredproof · cited by 6,101
- Finset.sumproof · cited by 5,195
- Set.preimageproof · cited by 4,946
- NNRealproof · cited by 4,310
- MeasurableSetproof · cited by 3,075
- one_mulproof · cited by 2,841
- Set.iUnionproof · cited by 2,483
Cited by16
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_const_mulproof · cited by 19
- MeasureTheory.lintegral_eq_iSup_eapprox_lintegralproof · cited by 7
- MeasureTheory.lintegral_trimproof · cited by 7
- Measurable.lintegral_kernel_prod_rightproof · cited by 5
- MeasureTheory.lintegral_withDensity_eq_lintegral_mulproof · cited by 5
- Measurable.lintegral_prod_right'proof · cited by 4
- MeasureTheory.Measure.lintegral_joinproof · cited by 2
- MeasureTheory.lintegral_iSup'proof · cited by 2
- MeasureTheory.lintegral_add_auxproof · cited by 1
- MeasureTheory.lintegral_iSup_aeproof · cited by 1
- MeasureTheory.lintegral_iSup_directed_of_measurableproof · cited by 1