Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.prod_flip_apply_eq_integral

∀ {X : Type u_2} {Y : Type u_3} {E : Type u_4} {F : Type u_5} {G : Type u_6} {mX : MeasurableSpace X}
  {mY : MeasurableSpace Y} [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 E} {ν : MeasureTheory.VectorMeasure Y F} [CompleteSpace G]
  [MeasureTheory.IsFiniteMeasure μ.variation] {B : F →L[ℝ] E →L[ℝ] G} {s : Set (X × Y)},
  MeasurableSet s → (μ.prod ν B.flip) s = ∫ᵛ (x : X), ν (Prod.mk x ⁻¹' s) ∂[B; μ]

Defined in

Mathlib.MeasureTheory.VectorMeasure.Prod

Cited by

0 results in Mathlib

Foundations

Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceMeasureTheory.IsFiniteMeasure