Theorems · Theorem · measure theory
MeasureTheory.Measure.addHaarScalarFactor_pos_of_isAddHaarMeasure
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [inst_2 : IsTopologicalAddGroup G]
[inst_3 : MeasurableSpace G] [inst_4 : BorelSpace G] (μ' μ : MeasureTheory.Measure G) [inst_5 : μ.IsAddHaarMeasure]
[inst_6 : μ'.IsAddHaarMeasure], 0 < μ'.addHaarScalarFactor μThe scalar factor between two left-invariant measures is non-zero when both measures are positive on open sets.
- Cited by
- 7 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.
Cites14
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
- AddGroupstatement and proof · cited by 4,410
- NNRealstatement · cited by 4,310
- MulZeroClass.zero_mulproof · cited by 1,625
- BorelSpacestatement and proof · cited by 1,602
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- one_ne_zeroproof · cited by 885
- MeasureTheory.Measure.IsAddHaarMeasurestatement and proof · cited by 255
- pos_iff_ne_zeroproof · cited by 180
- MeasureTheory.Measure.addHaarScalarFactorstatement and proof · cited by 58
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.addEquivAddHaarChar_eqproof · cited by 3
- MeasureTheory.Measure.addModularCharacterFun_eq_addHaarScalarFactorproof · cited by 3
- LinearMap.exists_map_addHaar_eq_smul_addHaar'proof · cited by 1
- MeasureTheory.lintegral_pow_le_pow_lintegral_fderivproof · cited by 1
- MeasureTheory.addEquivAddHaarChar_posproof · cited by 0
- MeasureTheory.Measure.addModularCharacterFun_posproof · cited by 0