Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.of_add_of_sdiff

∀ {α : Type u_1} {m : MeasurableSpace α} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M]
  {v : MeasureTheory.VectorMeasure α M} [T2Space M] {A B : Set α},
  MeasurableSet A → MeasurableSet B → A ⊆ B → v A + v (B \ A) = v B

Defined in: Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommMonoid TopologicalSpace T2Space

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
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
T2Spacestatement and proof · cited by 1,351
MeasureTheory.VectorMeasurestatement and proof · cited by 451
MeasurableSet.diffproof · cited by 53
Set.disjoint_sdiff_rightproof · cited by 23
MeasureTheory.VectorMeasure.of_unionproof · cited by 20
Set.union_sdiff_cancelproof · cited by 16

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.VectorMeasure.of_sdiffproof · cited by 2
MeasureTheory.SignedMeasure.exists_subset_restrict_nonposproof · cited by 1
MeasureTheory.VectorMeasure.of_add_of_diffproof · cited by 0