Theorems · Theorem · measure theory

MeasureTheory.integral_sub_left_eq_self

∀ {G : Type u_4} {E : Type u_5} [inst : MeasurableSpace G] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E]
  [inst_3 : AddGroup G] [MeasurableAdd G] [MeasurableNeg G] (f : G → E) (μ : MeasureTheory.Measure G) [μ.IsNegInvariant]
  [μ.IsAddLeftInvariant] (x' : G), ∫ (x : G), f (x' - x) ∂μ = ∫ (x : G), f x ∂μ

Defined in

Mathlib.MeasureTheory.Group.Integral

Cited by

1 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroupNormedSpaceAddGroupMeasurableAddMeasurableNegMeasureTheory.Measure.IsNegInvariantMeasureTheory.Measure.IsAddLeftInvariant