Theorems · Theorem · measure theory

MeasureTheory.Measure.haar.mul_left_index_le

∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [IsTopologicalGroup G] {K : Set G},
  IsCompact K →
    ∀ {V : Set G},
      (interior V).Nonempty →
        ∀ (g : G), 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 81 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
Finsetproof · cited by 13,712
Groupstatement and proof · cited by 6,238
Set.ofPredproof · cited by 6,101
Set.imagestatement and proof · cited by 5,609
Set.preimageproof · cited by 4,946
Set.rangeproof · cited by 4,705
Set.Nonemptystatement and proof · cited by 2,627
Set.iUnionproof · cited by 2,483
Finset.cardproof · cited by 2,327
mul_assocproof · cited by 1,667

Cited by1

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MeasureTheory.Measure.haar.is_left_invariant_indexproof · cited by 1