Theorems · Theorem · measure theory
MeasureTheory.ae_iff_measure_eq
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.IsFiniteMeasure μ]
{p : α → Prop}, MeasureTheory.NullMeasurableSet {a | p a} μ → ((∀ᵐ (a : α) ∂μ, p a) ↔ μ {a | p a} = μ Set.univ)- 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.
Cites14
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 and proof · cited by 6,101
- Set.univstatement · cited by 3,945
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.NullMeasurableSetstatement and proof · cited by 337
- Filter.eventually_iffproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_leproof · cited by 1
- MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_leproof · cited by 0
- MeasureTheory.ae_mem_iff_measure_eqproof · cited by 0