Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.empty
∀ {α : Type u_1} {m : MeasurableSpace α} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M]
(v : MeasureTheory.VectorMeasure α M), v ∅ = 0- Cited by
- 16 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · 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
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- MeasureTheory.VectorMeasure.empty'proof · cited by 1
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.enorm_measure_le_variationproof · cited by 15
- MeasureTheory.VectorMeasure.ennrealToMeasureproof · cited by 13
- MeasureTheory.VectorMeasure.restrict_emptyproof · cited by 8
- MeasurableEmbedding.variation_mapproof · cited by 3
- MeasureTheory.VectorMeasure.restrict_singletonproof · cited by 2
- MeasureTheory.VectorMeasure.hasSum_of_disjoint_iUnionproof · cited by 2
- MeasureTheory.VectorMeasure.of_ifproof · cited by 2
- MeasureTheory.VectorMeasure.prod_applyproof · cited by 2
- MeasureTheory.VectorMeasure.ext_of_generateFromproof · cited by 1
- MeasureTheory.VectorMeasure.MutuallySingular.zero_rightproof · cited by 1
- MeasureTheory.SignedMeasure.zero_mem_measureOfNegativesproof · cited by 1
- MeasureTheory.VectorMeasure.le_variationproof · cited by 1