Theorems · Theorem · measure theory
MeasureTheory.ae_restrict_iUnion_iff
∀ {α : Type u_2} {ι : Type u_6} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [Countable ι] (s : ι → Set α)
(p : α → Prop), (∀ᵐ (x : α) ∂μ.restrict (⋃ i, s i), p x) ↔ ∀ (i : ι), ∀ᵐ (x : α) ∂μ.restrict (s i), p x- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filter.Eventuallystatement and proof · cited by 3,134
- Set.iUnionstatement · cited by 2,483
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Countablestatement and proof · cited by 633
- MeasureTheory.ae_restrict_iUnion_eqproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_eq_zero_of_forall_setIntegral_isCompact_eq_zero'proof · cited by 1
- MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurableproof · cited by 1