Theorems · Theorem · measure theory

MeasureTheory.Lp.simpleFunc.memLp

∀ {α : Type u_1} {E : Type u_4} [inst : MeasurableSpace α] [inst_1 : NormedAddCommGroup E] {p : ENNReal}
  {μ : MeasureTheory.Measure α} (f : ↥(MeasureTheory.Lp.simpleFunc E p μ)),
  MeasureTheory.MemLp (⇑(MeasureTheory.Lp.simpleFunc.toSimpleFunc f)) p μ

toSimpleFunc f satisfies the predicate MemLp.

Defined in

Mathlib.MeasureTheory.Function.SimpleFuncDenseLp

Cited by

5 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroup