Theorems · Theorem · measure theory
MeasureTheory.Measure.toSphere_apply_aux
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E]
(μ : MeasureTheory.Measure E) (s : Set ↑(Metric.sphere 0 1)) (r : ↑(Set.Ioi 0)),
μ (Subtype.val '' ⇑(homeomorphUnitSphereProd E) ⁻¹' s ×ˢ Set.Iio r) = μ (Set.Ioo 0 ↑r • Subtype.val '' s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.Elemstatement and proof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- Compl.complstatement and proof · cited by 2,925
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.toSphere_apply'proof · cited by 3
- MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProdproof · cited by 2