Theorems · Theorem · measure theory
MeasureTheory.measurePreserving_smul
∀ {M : Type v} {α : Type w} {m : MeasurableSpace α} [inst : SMul M α] [MeasurableConstSMul M α] (c : M)
(μ : MeasureTheory.Measure α) [MeasureTheory.SMulInvariantMeasure M α μ],
MeasureTheory.MeasurePreserving (fun x => c • x) μ μ- Defined in
- Mathlib.MeasureTheory.Group.Action
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.MeasurePreservingstatement · cited by 259
- MeasureTheory.Measure.map_applyproof · cited by 139
- MeasureTheory.SMulInvariantMeasurestatement and proof · cited by 115
- MeasurableConstSMulstatement and proof · cited by 92
- MeasurableConstSMul.measurable_const_smulproof · cited by 12
Cited by17
Results whose statement or proof uses this declaration.
- aeconst_of_dense_setOfPred_preimage_smul_aeproof · cited by 4
- MeasureTheory.NullMeasurableSet.smulproof · cited by 4
- MeasureTheory.IsFundamentalDomain.setLIntegral_eq_tsum'proof · cited by 2
- QuotientGroup.integral_eq_integral_automorphizeproof · cited by 1
- MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum'proof · cited by 1
- MeasureTheory.IsFundamentalDomain.smul_of_commproof · cited by 1
- ergodic_smul_of_denseRange_powproof · cited by 1
- ergodic_smul_of_denseRange_zpowproof · cited by 1
- MeasureTheory.IsFundamentalDomain.aestronglyMeasurable_on_iffproof · cited by 1
- MeasureTheory.map_smulproof · cited by 1
- MeasureTheory.IsFundamentalDomain.integral_eq_tsum'proof · cited by 1
- MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum'proof · cited by 1