Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.restrict_empty
∀ {α : Type u_1} {mα : MeasurableSpace α} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M]
(v : MeasureTheory.VectorMeasure α M), v.restrict ∅ = 0- Cited by
- 8 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- MeasurableSetproof · cited by 3,075
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- zero_applyproof · cited by 251
- MeasureTheory.VectorMeasure.restrictstatement · cited by 139
- MeasureTheory.VectorMeasure.extproof · cited by 65
- MeasurableSet.emptyproof · cited by 58
- Set.inter_emptyproof · cited by 36
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.le_restrict_emptyproof · cited by 1
- MeasureTheory.VectorMeasure.restrict_unionproof · cited by 1
- MeasureTheory.VectorMeasure.variation_withDensity'proof · cited by 1
- MeasureTheory.VectorMeasure.setIntegral_biUnion_finsetproof · cited by 1
- MeasureTheory.VectorMeasure.restrict_le_restrict_countable_iUnionproof · cited by 1
- MeasureTheory.VectorMeasure.setIntegral_emptyproof · cited by 0
- MeasureTheory.VectorMeasure.IntegrableOn.emptyproof · cited by 0
- MeasureTheory.VectorMeasure.norm_setIntegral_le_of_norm_le_constproof · cited by 0