Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.variation_transpose_eq

∀ {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) [Nontrivial E],
  (∀ (x : E) (y : F), ‖(B x) y‖₊ = ‖x‖₊ * ‖y‖₊) → (μ.transpose B).variation = μ.variation

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

3 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNontrivial