Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.of_sdiff_of_sdiff_eq_zero

∀ {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 → v (B \ A) = 0 → v (A \ B) + v B = v A

Defined in: Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommMonoid TopologicalSpace T2Space

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Cites20

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
add_zeroproof · cited by 2,707
T2Spacestatement and proof · cited by 1,351
MeasureTheory.VectorMeasurestatement and proof · cited by 451
Set.inter_subset_leftproof · cited by 360
Set.inter_subset_rightproof · cited by 329
Set.inter_commproof · cited by 291

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.SignedMeasure.of_inter_eq_of_symmDiff_eq_zero_positiveproof · cited by 2
MeasureTheory.VectorMeasure.of_diff_of_diff_eq_zeroproof · cited by 0