Theorems · Theorem · measure theory

MeasureTheory.integral_map_equiv

∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} {β : Type u_6} [inst_2 : MeasurableSpace β] (e : α ≃ᵐ β) (f : β → G),
  ∫ (y : β), f y ∂MeasureTheory.Measure.map (⇑e) μ = ∫ (x : α), f (e x) ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

16 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpace