Theorems · Theorem · measure theory
MeasureTheory.measure_smul
∀ {G : Type u} {α : Type w} {m : MeasurableSpace α} [inst : Group G] [inst_1 : MulAction G α]
(μ : MeasureTheory.Measure α) [MeasureTheory.SMulInvariantMeasure G α μ] (c : G) (s : Set α), μ (c • s) = μ s- Defined in
- Mathlib.MeasureTheory.Group.Action
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Groupstatement and proof · cited by 6,238
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- MeasureTheory.SMulInvariantMeasurestatement and proof · cited by 115
- Set.preimage_smul_invproof · cited by 8
- MeasureTheory.measure_preimage_smulproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_smul_eq_zero_iffproof · cited by 1
- MeasureTheory.measure_univ_of_isMulLeftInvariantproof · cited by 1
- MeasureTheory.measure_inter_inv_smulproof · cited by 1
- MeasureTheory.measure_symmDiff_inv_smulproof · cited by 1
- MeasureTheory.measure_sdiff_inv_smulproof · cited by 1
- MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isMulLeftInvariantproof · cited by 1
- MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_compact_ne_zeroproof · cited by 1
- MeasureTheory.measure_union_inv_smulproof · cited by 1
- MeasureTheory.IsFundamentalDomain.measure_ne_zeroproof · cited by 0
- MeasureTheory.Subgroup.index_mul_measureproof · cited by 0