Theorems · Theorem · measure theory

MeasureTheory.Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq

∀ {α : Type u_1} [inst : MeasurableSpace α] {p : ENNReal} {μ : MeasureTheory.Measure α} {G : Type u_7}
  [inst_1 : NormedAddCommGroup G] [inst_2 : PartialOrder G] {f : ↥(MeasureTheory.Lp.simpleFunc G p μ)},
  0 ≤ f → ∃ f', 0 ≤ f' ∧ ↑↑↑f =ᵐ[μ] ⇑f'

Defined in

Mathlib.MeasureTheory.Function.SimpleFuncDenseLp

Cited by

1 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroupPartialOrder