Theorems · Theorem · measure theory

MeasureTheory.Measure.haar.is_left_invariant_addPrehaar

∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [inst_2 : IsTopologicalAddGroup G]
  {K₀ : TopologicalSpace.PositiveCompacts G} {U : Set G},
  (interior U).Nonempty →
    ∀ (g : G) (K : TopologicalSpace.Compacts G),
      MeasureTheory.Measure.haar.addPrehaar (↑K₀) U (TopologicalSpace.Compacts.map (fun x => g + x) ⋯ K) =
        MeasureTheory.Measure.haar.addPrehaar (↑K₀) U K

Defined in: Mathlib.MeasureTheory.Measure.Haar.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup TopologicalSpace IsTopologicalAddGroup

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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
Realstatement · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
SetLike.coestatement and proof · cited by 8,199
AddGroupstatement and proof · cited by 4,410
Set.Nonemptystatement and proof · cited by 2,627
IsTopologicalAddGroupstatement and proof · cited by 1,394
interiorstatement and proof · cited by 714
TopologicalSpace.Compactsstatement and proof · cited by 386
TopologicalSpace.PositiveCompactsstatement and proof · cited by 112
TopologicalSpace.Compacts.mapstatement · cited by 37
continuous_const_addstatement · cited by 23

Cited by1

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MeasureTheory.Measure.haar.is_left_invariant_addCHaarproof · cited by 1