Theorems · Theorem · measure theory
MeasureTheory.lintegral_congr_ae
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
f =ᵐ[μ] g → ∫⁻ (a : α), f a ∂μ = ∫⁻ (a : α), g a ∂μ- Cited by
- 95 results in Mathlib
- Foundations
- Depth 177 from the axioms, rests on 4,700 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.aestatement and proof · cited by 2,352
- le_antisymmproof · cited by 2,068
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.lintegralstatement · cited by 1,152
- Filter.EventuallyEq.symmproof · cited by 408
- Filter.EventuallyEq.leproof · cited by 46
- MeasureTheory.lintegral_mono_aeproof · cited by 36
Cited by95
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_eq_lintegral_of_nonneg_aeproof · cited by 31
- MeasureTheory.ofReal_integral_eq_lintegral_ofRealproof · cited by 22
- MeasureTheory.lintegral_prodproof · cited by 20
- MeasureTheory.lintegral_dirac'proof · cited by 19
- MeasureTheory.withDensity_congr_aeproof · cited by 19
- MeasureTheory.integral_toRealproof · cited by 15
- MeasureTheory.lintegral_map'proof · cited by 14
- MeasureTheory.lintegral_diracproof · cited by 13
- MeasureTheory.lintegral_add_left'proof · cited by 11
- MeasureTheory.lintegral_const_mul''proof · cited by 11
- MeasureTheory.setLIntegral_congr_fun_aeproof · cited by 11
- MeasureTheory.tendsto_setToFun_of_dominated_convergenceproof · cited by 5