Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.MutuallySingular.add_left
∀ {α : Type u_1} {m : MeasurableSpace α} {M : Type u_4} {N : Type u_5} [inst : AddCommMonoid M]
[inst_1 : TopologicalSpace M] [inst_2 : AddCommMonoid N] [inst_3 : TopologicalSpace N]
{v₁ v₂ : MeasureTheory.VectorMeasure α M} {w : MeasureTheory.VectorMeasure α N} [T2Space N]
[inst_5 : ContinuousAdd M], v₁.MutuallySingular w → v₂.MutuallySingular w → (v₁ + v₂).MutuallySingular w- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidstatement and proof · cited by 12,281
- MeasurableSetproof · cited by 3,075
- Compl.complproof · cited by 2,925
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- T2Spacestatement and proof · cited by 1,351
- ContinuousAddstatement and proof · cited by 777
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.singularPart_addproof · cited by 2
- MeasureTheory.VectorMeasure.MutuallySingular.add_rightproof · cited by 0