Theorems · Theorem · measure theory
MeasureTheory.addContent_empty
∀ {α : Type u_1} {C : Set (Set α)} {G : Type u_2} [inst : AddCommMonoid G] {m : MeasureTheory.AddContent G C}, m ∅ = 0- Defined in
- Mathlib.MeasureTheory.Measure.AddContent
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddCommMonoidstatement and proof · cited by 12,281
- MeasureTheory.AddContentstatement and proof · cited by 78
- MeasureTheory.AddContent.empty'proof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.AddContent.measureCaratheodorystatement and proof · cited by 2
- MeasureTheory.addContent_biUnion_leproof · cited by 2
- MeasureTheory.AddContent.isCaratheodory_inducedOuterMeasure_of_memstatement · cited by 1
- MeasureTheory.AddContent.isCaratheodory_ofFunction_of_memstatement and proof · cited by 1
- MeasureTheory.AddContent.measureCaratheodory_eqstatement · cited by 1
- MeasureTheory.AddContent.ofFunction_eqstatement and proof · cited by 1
- MeasureTheory.AddContent.inducedOuterMeasure_eqstatement and proof · cited by 1
- MeasureTheory.AddContent.measureCaratheodory_eq_inducedOuterMeasurestatement · cited by 0
- MeasureTheory.addContent_biUnion_eqproof · cited by 0
- MeasureTheory.AddContent.isCaratheodory_inducedOuterMeasurestatement and proof · cited by 0