Theorems · Theorem · measure theory
MeasureTheory.setIntegral_eq_zero_of_ae_eq_zero
∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
{f : X → E} {t : Set X} {μ : MeasureTheory.Measure X}, (∀ᵐ (x : X) ∂μ, x ∈ t → f x = 0) → ∫ (x : X) in t, f x ∂μ = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.integralstatement and proof · cited by 1,779
- Filter.univ_mem'proof · cited by 1,672
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Filter.mp_memproof · cited by 1,537
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.setIntegral_eq_zero_of_forall_eq_zeroproof · cited by 4