Theorems · Theorem · measure theory

MeasureTheory.Measure.sub_mem_nhds_zero_of_addHaar_pos

∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G]
  [inst_3 : MeasurableSpace G] [BorelSpace G] (μ : MeasureTheory.Measure G) [μ.IsAddHaarMeasure] [LocallyCompactSpace G]
  [μ.InnerRegular] (E : Set G), MeasurableSet E → 0 < μ E → E - E ∈ nhds 0

Steinhaus Theorem. In any locally compact group G with an inner regular Haar measure μ, for any measurable set E of positive measure, the set E - E is a neighbourhood of 0.

Defined in

Mathlib.MeasureTheory.Measure.Haar.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

AddGroupTopologicalSpaceIsTopologicalAddGroupMeasurableSpaceBorelSpaceMeasureTheory.Measure.IsAddHaarMeasureLocallyCompactSpaceMeasureTheory.Measure.InnerRegular