Theorems · Theorem · Lie groups
MeasureTheory.null_iff_of_isAddLeftInvariant
∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : TopologicalSpace G] [BorelSpace G] {μ : MeasureTheory.Measure G}
[inst_3 : AddGroup G] [IsTopologicalAddGroup G] [μ.IsAddLeftInvariant] [μ.Regular] {s : Set G},
IsOpen s → (μ s = 0 ↔ s = ∅ ∨ μ = 0)- Defined in
- Mathlib.MeasureTheory.Group.Measure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · 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
- AddGroupstatement and proof · cited by 4,410
- IsOpenstatement and proof · cited by 2,400
- BorelSpacestatement and proof · cited by 1,602
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- MeasureTheory.Measure.IsAddLeftInvariantstatement and proof · cited by 148
- MeasureTheory.Measure.Regularstatement and proof · cited by 61
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_ne_zero_iff_nonempty_of_isAddLeftInvariantproof · cited by 1