Theorems · Theorem · measure theory
MeasureTheory.ae_restrict_iUnion_eq
∀ {α : Type u_2} {ι : Type u_6} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [Countable ι] (s : ι → Set α),
MeasureTheory.ae (μ.restrict (⋃ i, s i)) = ⨆ i, MeasureTheory.ae (μ.restrict (s i))- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 198 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.
Cites17
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
- Filterstatement · cited by 8,121
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- MeasureTheory.aestatement · cited by 2,352
- le_antisymmproof · cited by 2,068
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- le_rflproof · cited by 1,558
- Countablestatement and proof · cited by 633
- iSup_leproof · cited by 190
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_restrict_biUnion_eqproof · cited by 3
- MeasureTheory.ae_restrict_union_eqproof · cited by 2
- MeasureTheory.ae_restrict_iUnion_iffproof · cited by 2
- MeasureTheory.ae_eq_restrict_iUnion_iffproof · cited by 0