Theorems · Theorem · measure theory
MeasureTheory.Measure.restrict_eq_zero
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α}, μ.restrict s = 0 ↔ μ s = 0- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 1,646
- MeasureTheory.Measure.measure_univ_eq_zeroproof · cited by 26
- MeasureTheory.Measure.restrict_apply_univproof · cited by 15
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.setLIntegral_measure_zeroproof · cited by 5
- MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae'proof · cited by 3
- MeasureTheory.Measure.restrict_zero_setproof · cited by 3
- MeasureTheory.setIntegral_measure_zeroproof · cited by 2
- MeasureTheory.pdf.IsUniform.pdf_eq_zero_of_measure_eq_zero_or_topproof · cited by 2
- ae_eq_const_or_exists_average_ne_complproof · cited by 2
- MeasureTheory.restrict_diracproof · cited by 2
- MeasureTheory.restrict_dirac'proof · cited by 2
- MeasureTheory.Measure.sub_apply_eq_zero_of_isHahnDecompositionproof · cited by 2
- ProbabilityTheory.condExp_generateFrom_singletonproof · cited by 1
- MeasureTheory.IntegrableOn.of_measure_zeroproof · cited by 1
- MeasureTheory.Measure.singularPart_eq_restrict'proof · cited by 1