Theorems · Theorem · real analysis

BoxIntegral.norm_integral_le_of_le_const

∀ {ι : Type u} {E : Type v} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {I : BoxIntegral.Box ι}
  [inst_2 : Fintype ι] {l : BoxIntegral.IntegrationParams} {f : (ι → ℝ) → E} {c : ℝ},
  (∀ x ∈ BoxIntegral.Box.Icc I, ‖f x‖ ≤ c) →
    ∀ (μ : MeasureTheory.Measure (ι → ℝ)) [inst_3 : MeasureTheory.IsLocallyFiniteMeasure μ],
      ‖BoxIntegral.integral I l f μ.toBoxAdditive.toSMul‖ ≤ μ.real ↑I * c

Defined in

Mathlib.Analysis.BoxIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceFintypeMeasureTheory.IsLocallyFiniteMeasure