Theorems · Theorem · measure theory

MeasurableEmbedding.integral_map

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

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

15 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace