Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.norm_setIntegral_le_of_norm_le_const

∀ {X : Type u_2} {E : Type u_3} {F : Type u_4} {G : Type u_5} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] [inst_2 : NormedAddCommGroup G] {μ : MeasureTheory.VectorMeasure X F} {f : X → E}
  {s : Set X} [inst_3 : NormedSpace ℝ E] [inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace ℝ G] {B : E →L[ℝ] F →L[ℝ] G}
  {C : ℝ} [h : MeasureTheory.IsFiniteMeasure (μ.variation.restrict s)],
  (∀ x ∈ s, ‖f x‖ ≤ C) → ‖∫ᵛ (x : X) in s, f x ∂[B; μ]‖ ≤ C * ‖B‖ * μ.variation.real s

Defined in

Mathlib.MeasureTheory.VectorMeasure.SetIntegral

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpaceMeasureTheory.IsFiniteMeasure