Theorems · Theorem · measure theory

MeasureTheory.Measure.haar.index_elim

∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [IsTopologicalGroup G] {K V : Set G},
  IsCompact K →
    (interior V).Nonempty → ∃ t, K ⊆ ⋃ g ∈ t, (fun h => g * h) ⁻¹' V ∧ t.card = MeasureTheory.Measure.haar.index K V

Defined in: Mathlib.MeasureTheory.Measure.Haar.Basic
Cited by: 5 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group TopologicalSpace IsTopologicalGroup

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Cites18

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
Finsetstatement and proof · cited by 13,712
Groupstatement and proof · cited by 6,238
Set.ofPredproof · cited by 6,101
Set.imageproof · cited by 5,609
Set.preimagestatement and proof · cited by 4,946
Set.Nonemptystatement and proof · cited by 2,627
Set.iUnionstatement and proof · cited by 2,483
Finset.cardstatement and proof · cited by 2,327
IsCompactstatement and proof · cited by 1,282
InfSet.sInfproof · cited by 935

Cited by5

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.haar.index_union_leproof · cited by 2
MeasureTheory.Measure.haar.mul_left_index_leproof · cited by 1
MeasureTheory.Measure.haar.index_monoproof · cited by 1
MeasureTheory.Measure.haar.index_union_eqproof · cited by 1
MeasureTheory.Measure.haar.le_index_mulproof · cited by 1