Theorems · Inductive type · measure theory
MeasureTheory.Measure.IsAddLeftInvariant
{G : Type u_1} → [inst : MeasurableSpace G] → [Add G] → MeasureTheory.Measure G → PropA measure μ on a measurable additive group is left invariant
if the measure of left translations of a set are equal to the measure of the set itself.
- Defined in
- Mathlib.MeasureTheory.Group.Defs
- Cited by
- 148 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- MeasurableSpaceAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
Cited by153
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaarScalarFactorstatement and proof · cited by 58
- MeasureTheory.measure_preimage_addstatement and proof · cited by 14
- MeasureTheory.Measure.addHaarMeasure_uniquestatement and proof · cited by 9
- MeasureTheory.map_add_left_eq_selfstatement and proof · cited by 9
- MeasureTheory.Measure.isAddLeftInvariant_eq_smulstatement and proof · cited by 8
- MeasureTheory.quasiMeasurePreserving_negstatement and proof · cited by 7
- MeasureTheory.integral_add_left_eq_selfstatement and proof · cited by 6
- MeasureTheory.convolution_flipstatement and proof · cited by 6
- MeasureTheory.Measure.addHaarScalarFactor_eq_mulstatement and proof · cited by 6
- Module.Basis.addHaar_eq_iffstatement and proof · cited by 5
- MeasureTheory.absolutelyContinuous_negstatement and proof · cited by 5
- MeasureTheory.measurePreserving_add_leftstatement and proof · cited by 5