Theorems · Theorem · measure theory
MeasureTheory.FinMeasAdditive.map_empty_eq_zero
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {β : Type u_8} [inst : AddCancelMonoid β]
{T : Set α → β}, MeasureTheory.FinMeasAdditive μ T → T ∅ = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCancelMonoid
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.
- DFunLike.coeproof · 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
- Top.topproof · cited by 9,680
- add_zeroproof · cited by 2,707
- LT.lt.neproof · cited by 872
- LE.le.trans_ltproof · cited by 795
- Eq.leproof · cited by 605
- MeasureTheory.measure_emptyproof · cited by 169
- Set.union_emptyproof · cited by 78
- MeasurableSet.emptyproof · cited by 58
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.map_setToSimpleFuncproof · cited by 6
- MeasureTheory.setToFun_of_le_map_of_stronglyMeasurableproof · cited by 2
- MeasureTheory.StronglyMeasurable.setToFun_prod_rightproof · cited by 1