Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.memLp_iff

∀ {α : Type u_1} {E : Type u_4} [inst : MeasurableSpace α] [inst_1 : NormedAddCommGroup E] {μ : MeasureTheory.Measure α}
  {p : ENNReal} {f : MeasureTheory.SimpleFunc α E},
  p ≠ 0 → p ≠ ⊤ → (MeasureTheory.MemLp (⇑f) p μ ↔ ∀ (y : E), y ≠ 0 → μ (⇑f ⁻¹' {y}) < ⊤)

Defined in

Mathlib.MeasureTheory.Function.SimpleFuncDenseLp

Cited by

4 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceNormedAddCommGroup