Theorems · Theorem · measure theory

MeasureTheory.Measure.toSphere_apply_univ

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E]
  (μ : MeasureTheory.Measure E) [BorelSpace E] [FiniteDimensional ℝ E] [μ.IsAddHaarMeasure],
  μ.toSphere Set.univ = ↑(Module.finrank ℝ E) * μ (Metric.ball 0 1)

Defined in: Mathlib.MeasureTheory.Constructions.HaarToSphere
Cited by: 2 results in Mathlib
Foundations: Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace MeasurableSpace BorelSpace FiniteDimensional MeasureTheory.Measure.IsAddHaarMeasure

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Cites25

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 · 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 and proof · cited by 9,879
Set.Elemstatement · cited by 7,166
Set.univstatement and proof · cited by 3,945
Nontrivialproof · cited by 2,416
FiniteDimensionalstatement and proof · cited by 1,854

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.toSphere_eq_zero_iff_finrankproof · cited by 1
MeasureTheory.Measure.toSphere_real_apply_univproof · cited by 1