Theorems · Theorem · measure theory
MeasureTheory.prob_compl_eq_zero_iff
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α}
[MeasureTheory.IsProbabilityMeasure μ], MeasurableSet s → (μ sᶜ = 0 ↔ μ s = 1)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 196 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 · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- Compl.complstatement · cited by 2,925
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.mem_ae_iff_prob_eq_oneproof · cited by 2
- MeasureTheory.IsZeroOneMeasure.exists_eq_diracproof · cited by 1
- MeasureTheory.dirac_eq_one_iff_memproof · cited by 0