Theorems · Theorem · measure theory

Topology.IsClosedEmbedding.integral_map_vectorMeasure

∀ {X : Type u_2} {E : Type u_4} {F : Type u_5} {G : Type u_6} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : NormedAddCommGroup G]
  [inst_5 : NormedSpace ℝ G] {μ : MeasureTheory.VectorMeasure X F} {B : E →L[ℝ] F →L[ℝ] G} {β : Type u_9}
  [inst_6 : MeasurableSpace β] {φ : X → β} [inst_7 : TopologicalSpace X] [BorelSpace X] [inst_9 : TopologicalSpace β]
  [BorelSpace β],
  Topology.IsClosedEmbedding φ → ∀ {f : β → E}, ∫ᵛ (y : β), f y ∂[B; μ.map φ] = ∫ᵛ (x : X), f (φ x) ∂[B; μ]

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

0 results in Mathlib

Foundations

Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceTopologicalSpaceBorelSpaceTopologicalSpaceBorelSpace