Theorems · Theorem · measure theory
MeasureTheory.Measure.measure_univ_eq_zero
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}, μ Set.univ = 0 ↔ μ = 0- Cited by
- 26 results in Mathlib
- Foundations
- Depth 197 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 · cited by 9,879
- Set.univstatement and proof · cited by 3,945
- MeasureTheory.measure_monoproof · cited by 338
- Set.subset_univproof · cited by 228
- bot_uniqueproof · cited by 57
Cited by26
Results whose statement or proof uses this declaration.
- MeasureTheory.IsProbabilityMeasure.ne_zeroproof · cited by 17
- MeasureTheory.Measure.restrict_eq_zeroproof · cited by 17
- MeasureTheory.Measure.measure_univ_ne_zeroproof · cited by 11
- MeasureTheory.eq_zero_or_isProbabilityMeasureproof · cited by 6
- MeasureTheory.FiniteMeasure.mass_zero_iffproof · cited by 5
- MeasureTheory.ae_eq_botproof · cited by 4
- MeasureTheory.measure_smul_averageproof · cited by 4
- MeasureTheory.Measure.MutuallySingular.self_iffproof · cited by 4
- MeasureTheory.Measure.absolutelyContinuous_zero_iffproof · cited by 3
- Ergodic.of_mem_extremePoints_measure_univ_eqproof · cited by 2
- MeasureTheory.withDensity_eq_zero_iffproof · cited by 2
- MeasureTheory.lintegral_strict_monoproof · cited by 1