Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.prod_apply

∀ {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} {B : E →L[ℝ] F →L[ℝ] G}
  [h : μ.HasProd ν B] {s : Set X} {t : Set Y}, (μ.prod ν B) (s ×ˢ t) = (B (μ s)) (ν t)

Defined in

Mathlib.MeasureTheory.VectorMeasure.Prod

Cited by

2 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasureTheory.VectorMeasure.HasProd