Theorems · Theorem · measure theory
MeasureTheory.setLIntegral_eq_zero
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal} {s : Set α},
MeasurableSet s → Set.EqOn f 0 s → ∫⁻ (x : α) in s, f x ∂μ = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 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.
- 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
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MulZeroClass.zero_mulproof · cited by 1,625
- MeasureTheory.lintegralstatement · cited by 1,152
- Set.EqOnstatement and proof · cited by 603
- Set.univ_interproof · cited by 258
- MeasureTheory.Measure.restrict_applyproof · cited by 159
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- ProbabilityTheory.lintegral_betaPDFproof · cited by 1