Theorems · Theorem · Lie groups
MeasureTheory.map_mul_left_eq_self
∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Mul G] (μ : MeasureTheory.Measure G) [μ.IsMulLeftInvariant]
(g : G), MeasureTheory.Measure.map (fun x => g * x) μ = μ- Defined in
- Mathlib.MeasureTheory.Group.Measure
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Measure.mapstatement · cited by 858
- MeasureTheory.Measure.IsMulLeftInvariantstatement and proof · cited by 118
- MeasureTheory.Measure.IsMulLeftInvariant.map_mul_left_eq_selfproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_preimage_mulproof · cited by 5
- MeasureTheory.integral_mul_left_eq_selfproof · cited by 4
- MeasureTheory.measurePreserving_mul_leftproof · cited by 4
- MeasureTheory.lintegral_mul_left_eq_selfproof · cited by 4
- MeasureTheory.measurePreserving_prod_mulproof · cited by 3
- MeasureTheory.isMulLeftInvariant_mapproof · cited by 2
- MeasureTheory.Integrable.comp_mul_leftproof · cited by 1
- MeasureTheory.map_mul_left_aeproof · cited by 1
- MeasureTheory.absolutelyContinuous_map_div_leftproof · cited by 0