Theorems · Theorem · measure theory

MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translates

∀ {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] {s : Set E} (u : ℕ → E),
  Bornology.IsBounded (Set.range u) → Pairwise (Function.onFun Disjoint fun n => {u n} + s) → MeasurableSet s → μ s = 0

If a set is disjoint from its translates by infinitely many bounded vectors, then it has measure zero.

Defined in

Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar

Cited by

1 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceFiniteDimensionalMeasureTheory.Measure.IsAddHaarMeasure