Theorems · Theorem · measure theory

MeasureTheory.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} [inst_2 : MeasurableSpace β] {φ : α → β},
  AEMeasurable φ μ →
    ∀ {f : β → G},
      MeasureTheory.AEStronglyMeasurable f (MeasureTheory.Measure.map φ μ) →
        ∫ (y : β), f y ∂MeasureTheory.Measure.map φ μ = ∫ (x : α), f (φ x) ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

67 results in Mathlib

Foundations

Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasurableSpace