Theorems · Theorem · measure theory

Topology.IsClosedEmbedding.setIntegral_map_vectorMeasure

∀ {X : Type u_2} {E : Type u_3} {F : Type u_4} {G : Type u_5} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] [inst_2 : NormedAddCommGroup G] {μ : MeasureTheory.VectorMeasure X F}
  [inst_3 : NormedSpace ℝ E] [inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace ℝ G] {B : E →L[ℝ] F →L[ℝ] G}
  [inst_6 : TopologicalSpace X] [BorelSpace X] {β : Type u_7} [inst_8 : MeasurableSpace β] [inst_9 : TopologicalSpace β]
  [BorelSpace β] {φ : X → β} {f : β → E} {s : Set β},
  MeasurableSet s →
    Topology.IsClosedEmbedding φ → ∫ᵛ (y : β) in s, f y ∂[B; μ.map φ] = ∫ᵛ (x : X) in φ ⁻¹' s, f (φ x) ∂[B; μ]

Defined in

Mathlib.MeasureTheory.VectorMeasure.SetIntegral

Cited by

0 results in Mathlib

Foundations

Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpaceTopologicalSpaceBorelSpaceMeasurableSpaceTopologicalSpaceBorelSpace