Theorems · Theorem · measure theory
MeasureTheory.measure_empty
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [MeasureTheory.OuterMeasureClass F α] {μ : F},
μ ∅ = 0- Defined in
- Mathlib.MeasureTheory.OuterMeasure.Basic
- Cited by
- 169 results in Mathlib
- Foundations
- Depth 106 from the axioms, rests on 1,984 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- ENNRealstatement and proof · cited by 9,879
- FunLikestatement and proof · cited by 2,560
- MeasureTheory.OuterMeasureClassstatement and proof · cited by 104
- MeasureTheory.OuterMeasureClass.measure_emptyproof · cited by 1
Cited by169
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_iUnion_leproof · cited by 39
- Disjoint.aedisjointproof · cited by 29
- MeasureTheory.Measure.restrict_emptyproof · cited by 24
- MeasureTheory.nonempty_of_measure_ne_zeroproof · cited by 22
- MeasureTheory.VectorMeasure.enorm_measure_le_variationproof · cited by 15
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- MeasureTheory.Measure.restrict_singletonproof · cited by 12
- MeasureTheory.measureReal_emptyproof · cited by 11
- Monotone.measure_iUnionproof · cited by 10
- ProbabilityTheory.Kernel.IndepSets.indepproof · cited by 9
- StieltjesFunction.measure_Iccproof · cited by 8
- MeasureTheory.Measure.restrict_sub_eq_restrict_sub_restrictproof · cited by 6