Mathlib Map

Theorems · Theorem · measure theory

MeasureTheory.lintegral_zero_measure

∀ {α : Type u_1} {m : MeasurableSpace α} (f : α → ENNReal), ∫⁻ (a : α), f a ∂0 = 0
Defined in
Mathlib.MeasureTheory.Integral.Lebesgue.Basic
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.

MeasureTheory.eLpNorm_measure_zero · cited by 13MeasureTheory.eLpNorm_mea…MeasureTheory.setLIntegral_measure_zero · cited by 5MeasureTheory.setLIntegra…MeasureTheory.Measure.MutuallySingular.compProd_of_left · cited by 5MutuallySingular.compProd…MeasureTheory.lintegral_of_isEmpty · cited by 5MeasureTheory.lintegral_o…MeasureTheory.laverage_zero_measure · cited by 4MeasureTheory.laverage_ze…MeasureTheory.lintegral_map_le · cited by 3MeasureTheory.lintegral_m…MeasureTheory.FiniteMeasure.zero_testAgainstNN_apply · cited by 3FiniteMeasure.zero_testAg…Manifold.pathELength_self · cited by 3Manifold.pathELength_selfMeasureTheory.setLIntegral_dirac · cited by 2MeasureTheory.setLIntegra…MeasureTheory.setLIntegral_dirac' · cited by 2MeasureTheory.setLIntegra…ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat · cited by 2ProbabilityTheory.setLInt…ProbabilityTheory.avgRisk_zero_left · cited by 2ProbabilityTheory.avgRisk…MeasureTheory.setLIntegral_tilted' · cited by 2MeasureTheory.setLIntegra…MeasureTheory.lintegral_finsetSum_measure · cited by 2MeasureTheory.lintegral_f…MeasureTheory.measure_mul_laverage · cited by 2MeasureTheory.measure_mul…DFunLike.coe · cited by 62936DFunLike.coeMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealiSup · cited by 2415iSupMeasureTheory.lintegral · cited by 1152MeasureTheory.lintegralMeasureTheory.SimpleFunc · cited by 411MeasureTheory.SimpleFunciSup_congr_Prop · cited by 247iSup_congr_PropciSup_const · cited by 43ciSup_constENNReal.iSup_zero · cited by 15ENNReal.iSup_zeroMeasureTheory.lintegral_def · cited by 15MeasureTheory.lintegral_d…MeasureTheory.SimpleFunc.lintegral_zero · cited by 1SimpleFunc.lintegral_zeroMeasureTheory.lintegral_zero_…CITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by34

Results whose statement or proof uses this declaration.