Theorems · Theorem · measure theory
MeasureTheory.measure_biUnion
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set β} {f : β → Set α},
s.Countable → s.PairwiseDisjoint f → (∀ b ∈ s, MeasurableSet (f b)) → μ (⋃ b ∈ s, f b) = ∑' (p : ↑s), μ (f ↑p)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Set.Elemstatement · cited by 7,166
- MeasurableSetstatement and proof · cited by 3,075
- Set.iUnionstatement · cited by 2,483
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- Set.Countablestatement and proof · cited by 545
- Set.PairwiseDisjointstatement and proof · cited by 275
Cited by7
Results whose statement or proof uses this declaration.
- VitaliFamily.FineSubfamilyOn.measure_le_tsum_of_absolutelyContinuousproof · cited by 2
- ProbabilityTheory.Kernel.densityProcess_fst_univ_aeproof · cited by 2
- BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAtproof · cited by 2
- MeasureTheory.tsum_measure_preimage_singletonproof · cited by 1
- Vitali.exists_disjoint_covering_aeproof · cited by 1
- MeasureTheory.measure_sUnionproof · cited by 1
- Besicovitch.exist_finset_disjoint_balls_large_measureproof · cited by 1