Theorems · Theorem · measure theory
MeasureTheory.lintegral_indicator
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
MeasurableSet s → ∀ (f : α → ENNReal), ∫⁻ (a : α), s.indicator f a ∂μ = ∫⁻ (a : α) in s, f a ∂μ- Cited by
- 47 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- iSupproof · cited by 2,415
- le_antisymmproof · cited by 2,068
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- le_rflproof · cited by 1,558
- MeasureTheory.lintegralstatement · cited by 1,152
- Set.indicatorstatement and proof · cited by 723
Cited by47
Results whose statement or proof uses this declaration.
- MeasureTheory.integrable_indicator_iffproof · cited by 30
- MeasureTheory.lintegral_indicator_oneproof · cited by 13
- MeasureTheory.eLpNorm_indicator_eq_eLpNorm_restrictproof · cited by 8
- MeasureTheory.setLIntegral_condLExpproof · cited by 8
- MeasureTheory.lintegral_trimproof · cited by 7
- MeasureTheory.lintegral_withDensity_eq_lintegral_mulproof · cited by 5
- MeasureTheory.withDensity_indicatorproof · cited by 5
- Measurable.lintegral_prod_right'proof · cited by 4
- MeasureTheory.Measure.prod_prod_leproof · cited by 4
- ProbabilityTheory.Kernel.swap_parallelCompproof · cited by 4
- ProbabilityTheory.Kernel.fst_compProdproof · cited by 4
- ProbabilityTheory.Kernel.compProd_restrictproof · cited by 4