Theorems · Theorem · measure theory

MeasureTheory.Measure.addHaar_closedBall_mul_of_pos

∀ {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 →
    ∀ (s : ℝ), μ (Metric.closedBall x (r * s)) = ENNReal.ofReal (r ^ Module.finrank ℝ E) * μ (Metric.closedBall 0 s)

Defined in

Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar

Cited by

0 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasure