Theorems · Definition · measure theory
MeasureTheory.SimpleFunc.lintegral
{α : Type u_1} → {_m : MeasurableSpace α} → MeasureTheory.SimpleFunc α ENNReal → MeasureTheory.Measure α → ENNRealIntegral of a simple function whose codomain is ℝ≥0∞.
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finset.sumproof · cited by 5,195
- Set.preimageproof · cited by 4,946
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- MeasureTheory.SimpleFunc.rangeproof · cited by 97
Cited by56
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_mono_aeproof · cited by 36
- MeasureTheory.lintegral_smul_measureproof · cited by 20
- MeasureTheory.lintegral_const_mulproof · cited by 19
- MeasureTheory.lintegral_mapproof · cited by 17
- MeasureTheory.lintegral_sum_measureproof · cited by 16
- MeasureTheory.lintegral_iSupproof · cited by 16
- MeasureTheory.SimpleFunc.lintegral_eq_lintegralstatement and proof · cited by 15
- MeasureTheory.lintegral_defstatement and proof · cited by 15
- MeasureTheory.lintegral_mono'proof · cited by 12
- MeasurableEmbedding.lintegral_mapproof · cited by 10
- MeasureTheory.SimpleFunc.map_lintegralstatement · cited by 7
- MeasureTheory.lintegral_eq_iSup_eapprox_lintegralstatement and proof · cited by 7