Theorems · Theorem · measure theory
MeasureTheory.IsZeroOrProbabilityMeasure.measure_univ
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
[self : MeasureTheory.IsZeroOrProbabilityMeasure μ], μ Set.univ = 0 ∨ μ Set.univ = 1- Cited by
- 4 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · 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 · cited by 3,945
- MeasureTheory.IsZeroOrProbabilityMeasurestatement and proof · cited by 46
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.prob_le_oneproof · cited by 11
- MeasureTheory.eq_zero_or_isProbabilityMeasureproof · cited by 6
- MeasureTheory.IsZeroOneMeasure.exists_eq_diracproof · cited by 1
- MeasureTheory.isZeroOrProbabilityMeasure_iffproof · cited by 0