Theorems · Theorem · measure theory
MeasureTheory.measure_smul_eq_zero_iff
∀ {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] {s : Set α} (c : G), μ (c • s) = 0 ↔ μ s = 0- Defined in
- Mathlib.MeasureTheory.Group.Action
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 and proof · 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
- MeasureTheory.measure_smulproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_smul_nullproof · cited by 1