Theorems · Theorem · measure theory

MeasureTheory.eLpNorm_indicator_sub_le_of_dist_bdd

∀ {α : Type u_1} {m0 : MeasurableSpace α} {p : ENNReal} {s : Set α} {β : Type u_9} [inst : NormedAddCommGroup β]
  (μ : autoParam (MeasureTheory.Measure α) MeasureTheory.eLpNorm_indicator_sub_le_of_dist_bdd._auto_1),
  p ≠ ⊤ →
    MeasurableSet s →
      ∀ {f g : α → β} {c : ℝ},
        0 ≤ c →
          (∀ x ∈ s, dist (f x) (g x) ≤ c) →
            MeasureTheory.eLpNorm (s.indicator (f - g)) p μ ≤ ENNReal.ofReal c * μ s ^ (1 / p.toReal)

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Indicator

Cited by

2 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup