Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.enorm_integral_le_of_enorm_le_const

∀ {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 : MeasureTheory.VectorMeasure X F} {B : E →L[ℝ] F →L[ℝ] G} {C : ENNReal},
  (∀ᵐ (x : X) ∂μ.variation, ‖f x‖ₑ ≤ C) → ‖∫ᵛ (x : X), f x ∂[B; μ]‖ₑ ≤ C * ‖B‖ₑ * μ.variation Set.univ

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

1 results in Mathlib

Foundations

Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace