Theorems · Theorem · measure theory

MeasureTheory.Measure.isMulInvariant_eq_smul_of_compactSpace

∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [inst_2 : IsTopologicalGroup G]
  [inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] [CompactSpace G] (μ' μ : MeasureTheory.Measure G)
  [inst_6 : μ.IsHaarMeasure] [inst_7 : μ'.IsMulLeftInvariant] [inst_8 : MeasureTheory.IsFiniteMeasureOnCompacts μ'],
  μ' = μ'.haarScalarFactor μ • μ

Uniqueness of Haar measures: Two Haar measures on a compact group coincide up to a multiplicative factor.

Defined in: Mathlib.MeasureTheory.Measure.Haar.Unique
Cited by: 1 results in Mathlib
Foundations: Depth 277 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Group IsTopologicalGroup MeasurableSpace BorelSpace CompactSpace MeasureTheory.Measure.IsHaarMeasure MeasureTheory.Measure.IsMulLeftInvariant MeasureTheory.IsFiniteMeasureOnCompacts

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
Groupstatement and proof · cited by 6,238
NNRealstatement · cited by 4,310
MeasurableSetproof · cited by 3,075
BorelSpacestatement and proof · cited by 1,602
CompactSpacestatement and proof · cited by 593
IsTopologicalGroupstatement and proof · cited by 469
MeasureTheory.Measure.extproof · cited by 308

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.mulEquivHaarChar_eq_one_of_compactSpaceproof · cited by 0