Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.edist_integral_le_lintegral_edist

∀ {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] {f g : X → E} {μ : MeasureTheory.VectorMeasure X F} {B : E →L[ℝ] F →L[ℝ] G},
  μ.Integrable f →
    μ.Integrable g →
      edist ∫ᵛ (a : X), f a ∂[B; μ] ∫ᵛ (a : X), g a ∂[B; μ] ≤ ‖B‖ₑ * ∫⁻ (a : X), edist (f a) (g a) ∂μ.variation

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

0 results in Mathlib

Foundations

Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace