Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.setIntegral_preimage_emb

∀ {X : Type u_1} {E : Type u_3} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  {μ : MeasureTheory.Measure X} {Y : Type u_5} {x : MeasurableSpace Y} {f : X → Y} {ν : MeasureTheory.Measure Y},
  MeasureTheory.MeasurePreserving f μ ν →
    MeasurableEmbedding f → ∀ (g : Y → E) (s : Set Y), ∫ (x : X) in f ⁻¹' s, g (f x) ∂μ = ∫ (y : Y) in s, g y ∂ν

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Set

Cited by

4 results in Mathlib

Foundations

Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace