Theorems · Theorem · measure theory

MeasureTheory.Measure.addHaar_closedBall

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : MeasurableSpace E] [BorelSpace E]
  [FiniteDimensional ℝ E] (μ : MeasureTheory.Measure E) [μ.IsAddHaarMeasure] (x : E) {r : ℝ},
  0 ≤ r → μ (Metric.closedBall x r) = ENNReal.ofReal (r ^ Module.finrank ℝ E) * μ (Metric.ball 0 1)

Defined in: Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
Cited by: 3 results in Mathlib
Foundations: Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace MeasurableSpace BorelSpace FiniteDimensional MeasureTheory.Measure.IsAddHaarMeasure

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Cites17

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
FiniteDimensionalstatement and proof · cited by 1,854
Module.finrankstatement and proof · cited by 1,770
BorelSpacestatement and proof · cited by 1,602
ENNReal.ofRealstatement and proof · cited by 863

Cited by3

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.addHaar_closedBall_eq_addHaar_ballproof · cited by 9
finite_integral_one_add_normproof · cited by 1
MeasureTheory.Measure.addHaar_sphere_of_ne_zeroproof · cited by 1