Theorems · Theorem · measure theory
MeasureTheory.mem_ae_iff_prob_eq_one
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α}
[MeasureTheory.IsProbabilityMeasure μ], MeasurableSet s → (s ∈ MeasureTheory.ae μ ↔ μ s = 1)- Cited by
- 2 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.
Cites11
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 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
- Filterstatement · cited by 8,121
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.aestatement · cited by 2,352
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.mem_ae_iffproof · cited by 16
- MeasureTheory.prob_compl_eq_zero_iffproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_iff_prob_eq_oneproof · cited by 2
- MeasureTheory.isProbabilityMeasure_comapproof · cited by 1