Theorems · Theorem · measure theory

MeasureTheory.ae_iff_prob_eq_one

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsProbabilityMeasure μ]
  {p : α → Prop}, Measurable p → ((∀ᵐ (a : α) ∂μ, p a) ↔ μ {a | p a} = 1)

Defined in: Mathlib.MeasureTheory.Measure.Typeclasses.Probability
Cited by: 2 results in Mathlib
Foundations: Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.IsProbabilityMeasure

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites12

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.ofPredstatement · cited by 6,101
Filter.Eventuallystatement · cited by 3,134
MeasureTheory.aestatement · cited by 2,352
Measurablestatement and proof · cited by 1,499
MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
Measurable.setOfproof · cited by 8
MeasureTheory.mem_ae_iff_prob_eq_oneproof · cited by 2

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mulproof · cited by 1
ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasureproof · cited by 1