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Theorems · Theorem · measure theory

MeasureTheory.measure_vadd

∀ {G : Type u} {α : Type w} {m : MeasurableSpace α} [inst : AddGroup G] [inst_1 : AddAction G α]
  (μ : MeasureTheory.Measure α) [MeasureTheory.VAddInvariantMeasure G α μ] (c : G) (s : Set α), μ (c +ᵥ s) = μ s
Defined in
Mathlib.MeasureTheory.Group.Action
Cited by
11 results in Mathlib
Foundations
Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddActionMeasureTheory.VAddInvariantMeasure

Around this declaration

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

MeasureTheory.measure_vadd_eq_zero_iff · cited by 3MeasureTheory.measure_vad…MeasureTheory.measure_univ_of_isAddLeftInvariant · cited by 2MeasureTheory.measure_uni…MeasureTheory.measure_inter_neg_vadd · cited by 2MeasureTheory.measure_int…MeasureTheory.IsAddFundamentalDomain.measure_ne_zero · cited by 2IsAddFundamentalDomain.me…MeasureTheory.measure_union_neg_vadd · cited by 1MeasureTheory.measure_uni…AddCircle.isAddFundamentalDomain_of_ae_ball · cited by 1AddCircle.isAddFundamenta…MeasureTheory.measure_symmDiff_neg_vadd · cited by 1MeasureTheory.measure_sym…MeasureTheory.measure_sdiff_neg_vadd · cited by 1MeasureTheory.measure_sdi…MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isAddLeftInvariant · cited by 1IsEverywherePos.IsGdelta_…MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_compact_ne_zero · cited by 1MeasureTheory.measure_isO…MeasureTheory.AddSubgroup.index_mul_measure · cited by 0AddSubgroup.index_mul_mea…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealAddGroup · cited by 4410AddGroupHVAdd.hVAdd · cited by 1820HVAdd.hVAddAddAction · cited by 820AddActionSet.vaddSet · cited by 403Set.vaddSetMeasureTheory.VAddInvariantMeasure · cited by 114MeasureTheory.VAddInvaria…Set.preimage_vadd_neg · cited by 10Set.preimage_vadd_negMeasureTheory.measure_preimage_vadd · cited by 3MeasureTheory.measure_pre…MeasureTheory.measure_vaddCITED BYCITES

Cites12

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

Cited by11

Results whose statement or proof uses this declaration.