Theorems · Theorem · measure theory

MeasureTheory.Measure.haar.is_left_invariant_addIndex

∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] {K : Set G},
  IsCompact K →
    ∀ (g : G) {V : Set G},
      (interior V).Nonempty →
        MeasureTheory.Measure.haar.addIndex ((fun h => g + h) '' K) V = MeasureTheory.Measure.haar.addIndex K V

Defined in: Mathlib.MeasureTheory.Measure.Haar.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup TopologicalSpace IsTopologicalAddGroup

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites17

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Set.imagestatement and proof · cited by 5,609
AddGroupstatement and proof · cited by 4,410
Set.Nonemptystatement and proof · cited by 2,627
le_antisymmproof · cited by 2,068
IsTopologicalAddGroupstatement and proof · cited by 1,394
IsCompactstatement and proof · cited by 1,282
interiorstatement and proof · cited by 714
Set.image_congrproof · cited by 533
Set.image_imageproof · cited by 140
IsCompact.imageproof · cited by 105

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.haar.is_left_invariant_addPrehaarproof · cited by 1