Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.restrict_union_add_inter
∀ {α : Type u_1} {mα : MeasurableSpace α} {M : Type u_4} [inst : TopologicalSpace M] [inst_1 : AddCommMonoid M]
[T2Space M] [inst_3 : ContinuousAdd M] {v : MeasureTheory.VectorMeasure α M} {s t : Set α},
MeasurableSet s → MeasurableSet t → v.restrict (s ∪ t) + v.restrict (s ∩ t) = v.restrict s + v.restrict t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- MeasurableSetstatement and proof · cited by 3,075
- add_commproof · cited by 1,535
- T2Spacestatement and proof · cited by 1,351
- ContinuousAddstatement and proof · cited by 777
- add_assocproof · cited by 746
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- MeasureTheory.VectorMeasure.restrictstatement and proof · cited by 139
- add_right_commproof · cited by 85
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.restrict_unionproof · cited by 1