Theorems · Inductive type · measure theory
MeasureTheory.Measure.IsMulLeftInvariant
{G : Type u_1} → [inst : MeasurableSpace G] → [Mul G] → MeasureTheory.Measure G → PropA measure μ on a measurable 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
- 118 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- MeasurableSpaceMul
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 by123
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.haarScalarFactorstatement and proof · cited by 31
- MeasureTheory.map_mul_left_eq_selfstatement and proof · cited by 9
- MeasureTheory.quasiMeasurePreserving_invstatement and proof · cited by 7
- MeasureTheory.absolutelyContinuous_invstatement and proof · cited by 5
- MeasureTheory.measure_preimage_mulstatement and proof · cited by 5
- MeasureTheory.Measure.haarScalarFactor.congr_simpstatement and proof · cited by 5
- MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closurestatement and proof · cited by 4
- MeasureTheory.Measure.exists_integral_isMulLeftInvariant_eq_smul_of_hasCompactSupportstatement and proof · cited by 4
- MeasureTheory.lintegral_mul_left_eq_selfstatement and proof · cited by 4
- MeasureTheory.Measure.haarMeasure_uniquestatement and proof · cited by 4
- MeasureTheory.Measure.haarScalarFactor_eq_integral_div_of_continuous_nonneg_posstatement and proof · cited by 4
- MeasureTheory.measure_mul_right_nullstatement and proof · cited by 4