Theorems · Theorem · measure theory

MeasureTheory.memLp_add_of_disjoint

∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] {f g : α → E},
  Disjoint (Function.support f) (Function.support g) →
    MeasureTheory.StronglyMeasurable f →
      MeasureTheory.StronglyMeasurable g →
        (MeasureTheory.MemLp (f + g) p μ ↔ MeasureTheory.MemLp f p μ ∧ MeasureTheory.MemLp g p μ)

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Indicator

Cited by

3 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroup