Theorems · Inductive type · Lie groups
MeasureTheory.Measure.IsNegInvariant
{G : Type u_1} → [inst : MeasurableSpace G] → [Neg G] → MeasureTheory.Measure G → PropA measure is invariant under negation if - μ = μ. Equivalently, this means that for all
measurable A we have μ (- A) = μ A, where - A is the pointwise negation of A.
- Defined in
- Mathlib.MeasureTheory.Group.Measure
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- MeasurableSpaceNeg
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 by44
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.map_neg_eq_selfstatement and proof · cited by 8
- MeasureTheory.convolution_flipstatement and proof · cited by 6
- MeasureTheory.Measure.measurePreserving_negstatement and proof · cited by 5
- MeasureTheory.IntegrableOn.comp_negstatement and proof · cited by 4
- MeasureTheory.integral_neg_eq_selfstatement and proof · cited by 4
- MeasureTheory.Measure.measurePreserving_sub_leftstatement and proof · cited by 3
- MeasureTheory.convolutionExistsAt_flipstatement and proof · cited by 3
- MeasureTheory.convolution_eq_swapstatement and proof · cited by 3
- HasCompactSupport.convolutionExists_leftstatement and proof · cited by 2
- MeasureTheory.Integrable.comp_negstatement and proof · cited by 2
- MeasureTheory.Integrable.comp_sub_leftstatement and proof · cited by 2
- MeasureTheory.lintegral_neg_eq_selfstatement and proof · cited by 2