Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.integral_comp

∀ {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} {x : MeasurableSpace β} {f : α → β} {ν : MeasureTheory.Measure β},
  MeasureTheory.MeasurePreserving f μ ν →
    MeasurableEmbedding f → ∀ (g : β → G), ∫ (x : α), g (f x) ∂μ = ∫ (y : β), g y ∂ν

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

11 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpace