Theorems · Theorem · measure theory
MeasureTheory.measure_union_le
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [MeasureTheory.OuterMeasureClass F α] {μ : F}
(s t : Set α), μ (s ∪ t) ≤ μ s + μ t- Defined in
- Mathlib.MeasureTheory.OuterMeasure.Basic
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- ENNRealstatement and proof · cited by 9,879
- FunLikestatement and proof · cited by 2,560
- Set.iUnionproof · cited by 2,483
- Finset.sum_singletonproof · cited by 251
- Finset.sum_insertproof · cited by 196
- MeasureTheory.OuterMeasureClassstatement and proof · cited by 104
- Set.union_eq_iUnionproof · cited by 28
- MeasureTheory.measure_iUnion_fintype_leproof · cited by 3
Cited by43
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_le_inter_add_sdiffproof · cited by 7
- MeasureTheory.Measure.eq_singularPartproof · cited by 6
- MeasureTheory.withDensity_absolutelyContinuous'proof · cited by 5
- MeasureTheory.measure_mono_aeproof · cited by 5
- MeasureTheory.measure_eq_measure_of_between_null_sdiffproof · cited by 4
- MeasureTheory.Measure.absolutelyContinuous_withDensity_rnDerivproof · cited by 4
- MeasureTheory.measure_symmDiff_leproof · cited by 4
- MeasureTheory.measureReal_union_leproof · cited by 4
- MeasureTheory.measure_sdiff_eq_topproof · cited by 3
- MeasureTheory.Measure.restrict_union_leproof · cited by 3
- MeasureTheory.measure_union_lt_topproof · cited by 3