Theorems · Theorem · measure theory
MeasureTheory.lintegral_indicator_one
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
MeasurableSet s → ∫⁻ (a : α), s.indicator 1 a ∂μ = μ s- Cited by
- 13 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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 · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- one_mulproof · cited by 2,841
- MeasureTheory.lintegralstatement · cited by 1,152
- Set.indicatorstatement · cited by 723
- Set.univ_interproof · cited by 258
- MeasureTheory.Measure.restrict_applyproof · cited by 159
- MeasureTheory.lintegral_constproof · cited by 123
Cited by13
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.compProd_applyproof · cited by 31
- ProbabilityTheory.Kernel.id_compproof · cited by 9
- MeasureTheory.Measure.mconv_absolutelyContinuousproof · cited by 3
- MeasureTheory.Measure.conv_absolutelyContinuousproof · cited by 3
- MeasureTheory.tendsto_measure_of_ae_tendsto_indicatorproof · cited by 2
- NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integralproof · cited by 1
- Real.volume_preserving_transvectionStructproof · cited by 1
- ProbabilityTheory.Kernel.copy_comp_apply_prodproof · cited by 1
- ProbabilityTheory.Kernel.trajContent_eq_lmarginalPartialTrajproof · cited by 1
- MeasureTheory.Measure.ext_iff_lintegralproof · cited by 1
- bergelson'proof · cited by 1
- MeasureTheory.Measure.compProd_idproof · cited by 1