Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.nndist_integral_add_vectorMeasure_le_lintegral

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

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

0 results in Mathlib

Foundations

Depth 249 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace