Theorems · Theorem · measure theory
MeasureTheory.measure_biUnion_lt_top
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {s : Set β} {f : β → Set α},
s.Finite → (∀ i ∈ s, μ (f i) < ⊤) → μ (⋃ i ∈ s, f i) < ⊤- Cited by
- 8 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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 and proof · 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 and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Set.iUnionstatement and proof · cited by 2,483
- Set.extproof · cited by 2,266
- Set.Finitestatement and proof · cited by 1,814
- LE.le.trans_ltproof · cited by 795
- DFunLikeproof · cited by 576
- Set.Finite.toFinsetproof · cited by 351
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_spanningSets_lt_topproof · cited by 25
- MeasureTheory.SimpleFunc.finMeasSupp_iffproof · cited by 6
- MeasureTheory.measure_lt_top_of_isCompact_of_isAddLeftInvariantproof · cited by 1
- MeasureTheory.FinMeasAdditive.map_iUnion_fin_meas_set_eq_sumproof · cited by 1
- MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariantproof · cited by 1
- MeasureTheory.measure_biUnion_ne_topproof · cited by 0