Theorems · Theorem · measure theory
MeasureTheory.lintegral_zero_measure
∀ {α : Type u_1} {m : MeasurableSpace α} (f : α → ENNReal), ∫⁻ (a : α), f a ∂0 = 0- Cited by
- 34 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.
Cites12
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 · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- iSupproof · cited by 2,415
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.SimpleFuncproof · cited by 411
- iSup_congr_Propproof · cited by 247
- ciSup_constproof · cited by 43
- ENNReal.iSup_zeroproof · cited by 15
- MeasureTheory.lintegral_defproof · cited by 15
- MeasureTheory.SimpleFunc.lintegral_zeroproof · cited by 1
Cited by34
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNorm_measure_zeroproof · cited by 13
- MeasureTheory.setLIntegral_measure_zeroproof · cited by 5
- MeasureTheory.Measure.MutuallySingular.compProd_of_leftproof · cited by 5
- MeasureTheory.lintegral_of_isEmptyproof · cited by 5
- MeasureTheory.laverage_zero_measureproof · cited by 4
- MeasureTheory.lintegral_map_leproof · cited by 3
- MeasureTheory.FiniteMeasure.zero_testAgainstNN_applyproof · cited by 3
- Manifold.pathELength_selfproof · cited by 3
- MeasureTheory.setLIntegral_diracproof · cited by 2
- MeasureTheory.setLIntegral_dirac'proof · cited by 2
- ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRatproof · cited by 2
- ProbabilityTheory.avgRisk_zero_leftproof · cited by 2