Theorems · Theorem · measure theory

MeasurableEmbedding.integrable_map_vectorMeasure

∀ {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_9} [inst_2 : MeasurableSpace β]
  {φ : X → β}, MeasurableEmbedding φ → ∀ {f : β → E}, (μ.map φ).Integrable f ↔ μ.Integrable (f ∘ φ)

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

1 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedAddCommGroupMeasurableSpace