Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.Integrable.map

∀ {X : Type u_2} {E : Type u_4} {F : Type u_5} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] {μ : MeasureTheory.VectorMeasure X F} {β : Type u_10} [inst_2 : MeasurableSpace β]
  {φ : X → β} {f : β → E},
  MeasureTheory.AEStronglyMeasurable f (MeasureTheory.Measure.map φ μ.variation) →
    μ.Integrable (f ∘ φ) → (μ.map φ).Integrable f

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

0 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupMeasurableSpace