Theorems · Theorem · measure theory

MeasureTheory.Measure.addHaar_closedBall_eq_addHaar_ball

∀ {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] [Nontrivial E] (x : E) (r : ℝ),
  μ (Metric.closedBall x r) = μ (Metric.ball x r)

Defined in

Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar

Cited by

9 results in Mathlib

Foundations

Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasureNontrivial