Theorems · Theorem · measure theory

MeasureTheory.Measure.haar.addIndex_union_le

∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G]
  (K₁ K₂ : TopologicalSpace.Compacts G) {V : Set G},
  (interior V).Nonempty →
    MeasureTheory.Measure.haar.addIndex (K₁.carrier ∪ K₂.carrier) V ≤
      MeasureTheory.Measure.haar.addIndex K₁.carrier V + MeasureTheory.Measure.haar.addIndex K₂.carrier V

Defined in: Mathlib.MeasureTheory.Measure.Haar.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup TopologicalSpace IsTopologicalAddGroup

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Cites21

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
Set.preimageproof · cited by 4,946
AddGroupstatement and proof · cited by 4,410
Set.Nonemptystatement and proof · cited by 2,627
Set.iUnionproof · cited by 2,483
Finset.cardproof · cited by 2,327
IsTopologicalAddGroupstatement and proof · cited by 1,394
le_transproof · cited by 985
interiorstatement and proof · cited by 714
TopologicalSpace.Compactsstatement and proof · cited by 386

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.haar.addIndex_union_eqproof · cited by 1
MeasureTheory.Measure.haar.addPrehaar_sup_leproof · cited by 1