Theorems · Theorem · Lie groups
MeasureTheory.map_add_left_eq_self
∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Add G] (μ : MeasureTheory.Measure G) [μ.IsAddLeftInvariant]
(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.IsAddLeftInvariantstatement and proof · cited by 148
- MeasureTheory.Measure.IsAddLeftInvariant.map_add_left_eq_selfproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_preimage_addproof · cited by 14
- MeasureTheory.integral_add_left_eq_selfproof · cited by 6
- MeasureTheory.measurePreserving_add_leftproof · cited by 5
- MeasureTheory.lintegral_add_left_eq_selfproof · cited by 4
- MeasureTheory.measurePreserving_prod_addproof · cited by 3
- MeasureTheory.isAddLeftInvariant_mapproof · cited by 2
- MeasureTheory.Integrable.comp_add_leftproof · cited by 2
- MeasureTheory.map_add_left_aeproof · cited by 1
- MeasureTheory.absolutelyContinuous_map_sub_leftproof · cited by 0