Theorems · Theorem · measure theory
MeasureTheory.integral_indicator_const
∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
{μ : MeasureTheory.Measure X} [CompleteSpace E] (e : E) ⦃s : Set X⦄,
MeasurableSet s → ∫ (x : X), s.indicator (fun x => e) x ∂μ = μ.real s • e- Cited by
- 7 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetstatement and proof · cited by 3,075
- CompleteSpacestatement and proof · cited by 2,532
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.Measure.restrictproof · cited by 1,646
- Set.indicatorstatement · cited by 723
- MeasureTheory.Measure.realstatement and proof · cited by 530
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_indicator_oneproof · cited by 5
- MeasureTheory.setIntegral_indicatorConstLpproof · cited by 4
- ProbabilityTheory.condDistrib_ae_eq_condExpproof · cited by 2
- ContinuousLinearMap.integral_comp_commSLproof · cited by 2
- ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eqproof · cited by 1