Theorems · Theorem · measure theory

MeasureTheory.integral_smul_eq_self

∀ {α : Type u_3} {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {G : Type u_7}
  [inst_2 : Group G] [inst_3 : MeasurableSpace α] [inst_4 : MulAction G α] [MeasurableConstSMul G α]
  {μ : MeasureTheory.Measure α} [MeasureTheory.SMulInvariantMeasure G α μ] (f : α → E) {g : G},
  ∫ (x : α), f (g • x) ∂μ = ∫ (x : α), f x ∂μ

Defined in

Mathlib.MeasureTheory.Group.Integral

Cited by

0 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceGroupMeasurableSpaceMulActionMeasurableConstSMulMeasureTheory.SMulInvariantMeasure