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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
Defined in
Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by
16 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidTopologicalSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.VectorMeasure.enorm_measure_le_variation · cited by 15VectorMeasure.enorm_measu…MeasureTheory.VectorMeasure.ennrealToMeasure · cited by 13VectorMeasure.ennrealToMe…MeasureTheory.VectorMeasure.restrict_empty · cited by 8VectorMeasure.restrict_em…MeasurableEmbedding.variation_map · cited by 3MeasurableEmbedding.varia…MeasureTheory.VectorMeasure.restrict_singleton · cited by 2VectorMeasure.restrict_si…MeasureTheory.VectorMeasure.hasSum_of_disjoint_iUnion · cited by 2VectorMeasure.hasSum_of_d…MeasureTheory.VectorMeasure.of_if · cited by 2VectorMeasure.of_ifMeasureTheory.VectorMeasure.prod_apply · cited by 2VectorMeasure.prod_applyMeasureTheory.VectorMeasure.ext_of_generateFrom · cited by 1VectorMeasure.ext_of_gene…MeasureTheory.VectorMeasure.MutuallySingular.zero_right · cited by 1MutuallySingular.zero_rig…MeasureTheory.SignedMeasure.zero_mem_measureOfNegatives · cited by 1SignedMeasure.zero_mem_me…MeasureTheory.VectorMeasure.le_variation · cited by 1VectorMeasure.le_variationMeasureTheory.VectorMeasure.ennrealToMeasure_zero · cited by 1VectorMeasure.ennrealToMe…MeasureTheory.VectorMeasure.stronglyMeasurable_vectorMeasure_prodMk_left · cited by 1VectorMeasure.stronglyMea…MeasureTheory.VectorMeasure.apply_eq_zero_of_isEmpty · cited by 0VectorMeasure.apply_eq_ze…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceAddCommMonoid · cited by 12281AddCommMonoidMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasureTheory.VectorMeasure.empty' · cited by 1VectorMeasure.empty'VectorMeasure.emptyCITED BYCITES

Cites7

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

Cited by17

Results whose statement or proof uses this declaration.