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Theorems · Definition · measure theory

MeasureTheory.SimpleFunc.lintegral

{α : Type u_1} → {_m : MeasurableSpace α} → MeasureTheory.SimpleFunc α ENNReal → MeasureTheory.Measure α → ENNReal

Integral of a simple function whose codomain is ℝ≥0∞.

Defined in
Mathlib.MeasureTheory.Function.SimpleFunc
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.

MeasureTheory.lintegral_mono_ae · cited by 36MeasureTheory.lintegral_m…MeasureTheory.lintegral_smul_measure · cited by 20MeasureTheory.lintegral_s…MeasureTheory.lintegral_const_mul · cited by 19MeasureTheory.lintegral_c…MeasureTheory.lintegral_map · cited by 17MeasureTheory.lintegral_m…MeasureTheory.lintegral_sum_measure · cited by 16MeasureTheory.lintegral_s…MeasureTheory.lintegral_iSup · cited by 16MeasureTheory.lintegral_i…MeasureTheory.SimpleFunc.lintegral_eq_lintegral · cited by 15SimpleFunc.lintegral_eq_l…MeasureTheory.lintegral_def · cited by 15MeasureTheory.lintegral_d…MeasureTheory.lintegral_mono' · cited by 12MeasureTheory.lintegral_m…MeasurableEmbedding.lintegral_map · cited by 10MeasurableEmbedding.linte…MeasureTheory.SimpleFunc.map_lintegral · cited by 7SimpleFunc.map_lintegralMeasureTheory.lintegral_eq_iSup_eapprox_lintegral · cited by 7MeasureTheory.lintegral_e…MeasureTheory.SimpleFunc.lintegral_mono · cited by 6SimpleFunc.lintegral_monoMeasureTheory.lintegral_eq_nnreal · cited by 6MeasureTheory.lintegral_e…MeasureTheory.SimpleFunc.lintegralₗ · cited by 5SimpleFunc.lintegralₗDFunLike.coe · cited by 62936DFunLike.coeMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealFinset.sum · cited by 5195Finset.sumSet.preimage · cited by 4946Set.preimageMeasureTheory.SimpleFunc · cited by 411MeasureTheory.SimpleFuncMeasureTheory.SimpleFunc.range · cited by 97SimpleFunc.rangeSimpleFunc.lintegralCITED BYCITES

Cites8

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

Cited by56

Results whose statement or proof uses this declaration.