Theorems · Theorem · measure theory

MeasureTheory.MemLp.eLpNorm_indicator_le_of_meas

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {p : ENNReal} {f : α → β},
  1 ≤ p →
    p ≠ ⊤ →
      MeasureTheory.MemLp f p μ →
        MeasureTheory.StronglyMeasurable f →
          ∀ {ε : ℝ},
            0 < ε →
              ∃ δ,
                ∃ (_ : 0 < δ),
                  ∀ (s : Set α),
                    MeasurableSet s →
                      μ s ≤ ENNReal.ofReal δ → MeasureTheory.eLpNorm (s.indicator f) p μ ≤ ENNReal.ofReal ε

This lemma is superseded by MeasureTheory.MemLp.eLpNorm_indicator_le which does not require measurability on f.

Defined in

Mathlib.MeasureTheory.Function.UniformIntegrable

Cited by

1 results in Mathlib

Foundations

Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup