Theorems · Theorem · measure theory
MeasureTheory.Measure.addHaar_closedBall_center
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : MeasurableSpace E] [BorelSpace E] (μ : MeasureTheory.Measure E)
[μ.IsAddHaarMeasure] (x : E) (r : ℝ), μ (Metric.closedBall x r) = μ (Metric.closedBall 0 r)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 203 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 and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.preimageproof · cited by 4,946
- BorelSpacestatement and proof · cited by 1,602
- sub_selfproof · cited by 996
- Metric.closedBallstatement and proof · cited by 704
- MeasureTheory.Measure.IsAddHaarMeasurestatement and proof · cited by 255
Cited by6
Results whose statement or proof uses this declaration.
- AddCircle.volume_closedBallproof · cited by 4
- NormedAddCommGroup.exists_norm_nsmul_leproof · cited by 1
- MeasureTheory.Measure.addHaar_real_closedBall_centerproof · cited by 1
- MeasureTheory.Measure.addHaar_closedBall_mulproof · cited by 1
- MeasureTheory.Measure.addHaar_closedBall_mul_of_posproof · cited by 0