Theorems · Theorem · measure theory
MeasureTheory.Measure.haarScalarFactor_pos_of_isHaarMeasure
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [inst_2 : IsTopologicalGroup G]
[inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] (μ' μ : MeasureTheory.Measure G) [inst_5 : μ.IsHaarMeasure]
[inst_6 : μ'.IsHaarMeasure], 0 < μ'.haarScalarFactor μThe scalar factor between two left-invariant measures is non-zero when both measures are positive on open sets.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Groupstatement and proof · cited by 6,238
- NNRealstatement · cited by 4,310
- MulZeroClass.zero_mulproof · cited by 1,625
- BorelSpacestatement and proof · cited by 1,602
- IsTopologicalGroupstatement and proof · cited by 469
- pos_iff_ne_zeroproof · cited by 180
- MeasureTheory.Measure.IsHaarMeasurestatement and proof · cited by 63
- MeasureTheory.Measure.haarScalarFactorstatement and proof · cited by 31
- MeasureTheory.Measure.haarScalarFactor_selfproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.mulEquivHaarChar_eqproof · cited by 3
- MeasureTheory.Measure.modularCharacterFun_eq_haarScalarFactorproof · cited by 3
- MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePosproof · cited by 1
- MeasureTheory.Measure.modularCharacterFun_posproof · cited by 0
- MeasureTheory.mulEquivHaarChar_posproof · cited by 0