Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.variation_prod_le

∀ {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} [CompleteSpace G]
  [MeasureTheory.IsFiniteMeasure μ.variation] [MeasureTheory.SFinite ν.variation],
  (μ.prod ν B).variation ≤ ‖B‖ₑ • μ.variation.prod ν.variation

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.IsFiniteMeasureMeasureTheory.SFinite