Theorems · Theorem · measure theory

MeasureTheory.Measure.haar.is_left_invariant_index

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

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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
Groupstatement and proof · cited by 6,238
Set.imagestatement and proof · cited by 5,609
Set.Nonemptystatement and proof · cited by 2,627
le_antisymmproof · cited by 2,068
IsCompactstatement and proof · cited by 1,282
interiorstatement and proof · cited by 714
Set.image_congrproof · cited by 533
IsTopologicalGroupstatement and proof · cited by 469
Set.image_imageproof · cited by 140
IsCompact.imageproof · cited by 105

Cited by1

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MeasureTheory.Measure.haar.is_left_invariant_prehaarproof · cited by 1