Theorems · Inductive type · Lie groups
MeasureTheory.Measure.IsInvInvariant
{G : Type u_1} → [inst : MeasurableSpace G] → [Inv G] → MeasureTheory.Measure G → PropA measure is invariant under inversion if μ⁻¹ = μ. Equivalently, this means that for all
measurable A we have μ (A⁻¹) = μ A, where A⁻¹ is the pointwise inverse of A.
- Defined in
- Mathlib.MeasureTheory.Group.Measure
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- MeasurableSpaceInv
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 by26
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.map_inv_eq_selfstatement and proof · cited by 5
- MeasureTheory.IntegrableOn.comp_invstatement and proof · cited by 4
- MeasureTheory.Measure.measurePreserving_div_leftstatement and proof · cited by 2
- MeasureTheory.Measure.measurePreserving_invstatement and proof · cited by 2
- MeasureTheory.Measure.IsInvInvariant.inv_eq_selfstatement and proof · cited by 2
- MeasureTheory.lintegral_inv_eq_selfstatement and proof · cited by 2
- MeasureTheory.Integrable.comp_div_leftstatement and proof · cited by 1
- MeasureTheory.Integrable.comp_invstatement and proof · cited by 1
- MeasureTheory.Measure.measurePreserving_mul_right_invstatement and proof · cited by 1
- MeasureTheory.Measure.measure_invstatement and proof · cited by 1
- MeasureTheory.integral_inv_eq_selfstatement and proof · cited by 1
- MeasureTheory.Measure.map_div_left_eq_selfstatement and proof · cited by 1