Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.restrict_add_restrict_compl

∀ {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} {i : Set α},
  MeasurableSet i → v.restrict i + v.restrict iᶜ = v

Defined in: Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace AddCommMonoid T2Space ContinuousAdd

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Cites21

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

DFunLike.coeproof · 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
Compl.complstatement and proof · cited by 2,925
T2Spacestatement and proof · cited by 1,351
ContinuousAddstatement and proof · cited by 777
MeasureTheory.VectorMeasurestatement and proof · cited by 451
MeasurableSet.complproof · cited by 172
MeasurableSet.interproof · cited by 167

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.sub_toSignedMeasure_eq_toSignedMeasure_subproof · cited by 0