Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.transpose_map

∀ {X : Type u_2} {Y : Type u_3} {E : Type u_4} {F : Type u_5} {G : Type u_6} {mX : MeasurableSpace X}
  [inst : MeasurableSpace Y] [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E] [inst_3 : NormedAddCommGroup F]
  [inst_4 : NormedSpace ℝ F] [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace ℝ G]
  (μ : MeasureTheory.VectorMeasure X F) (B : E →L[ℝ] F →L[ℝ] G) {φ : X → Y},
  (μ.map φ).transpose B = (μ.transpose B).map φ

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

2 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace