Theorems · Theorem · measure theory
MeasureTheory.setLIntegral_measure_zero
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (s : Set α) (f : α → ENNReal),
μ s = 0 → ∫⁻ (x : α) in s, f x ∂μ = 0- Cited by
- 5 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.
Cites9
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 and proof · cited by 9,879
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.lintegral_zero_measureproof · cited by 34
- MeasureTheory.Measure.restrict_eq_zeroproof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.withDensity_absolutelyContinuousproof · cited by 40
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- ProbabilityTheory.Kernel.withDensity_rnDeriv_mutuallySingularSetSliceproof · cited by 3
- MeasureTheory.Measure.absolutelyContinuous_of_compProdproof · cited by 3
- MeasureTheory.setLAverage_le_essSupproof · cited by 1