Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.setLIntegral_comp_emb

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {ν : MeasureTheory.Measure β} {g : α → β},
  MeasureTheory.MeasurePreserving g μ ν →
    MeasurableEmbedding g → ∀ (f : β → ENNReal) (s : Set α), ∫⁻ (a : α) in s, f (g a) ∂μ = ∫⁻ (b : β) in g '' s, f b ∂ν

Defined in

Mathlib.MeasureTheory.Integral.Lebesgue.Map

Cited by

5 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace