Theorems · Theorem · measure theory
MeasureTheory.Measure.IsMulLeftInvariant.map_mul_left_eq_self
∀ {G : Type u_1} {inst : MeasurableSpace G} {inst_1 : Mul G} {μ : MeasureTheory.Measure G} [self : μ.IsMulLeftInvariant]
(g : G), MeasureTheory.Measure.map (fun x => g * x) μ = μ- Defined in
- Mathlib.MeasureTheory.Group.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.map_mul_left_eq_selfproof · cited by 9
- MeasureTheory.Measure.mconv_absolutelyContinuousproof · cited by 3
- MeasureTheory.forall_measure_preimage_mul_iffproof · cited by 1
- MeasureTheory.Measure.IsMulLeftInvariant.comapproof · cited by 0