Theorems · Theorem · functional analysis

MeasureTheory.AEEqFun.compMeasurePreserving_mem_Lp

∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] {β : Type u_7} [inst_1 : MeasurableSpace β] {μb : MeasureTheory.Measure β}
  {g : β →ₘ[μb] E},
  g ∈ MeasureTheory.Lp E p μb →
    ∀ {f : α → β} (hf : MeasureTheory.MeasurePreserving f μ μb), g.compMeasurePreserving f hf ∈ MeasureTheory.Lp E p μ

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

0 results in Mathlib

Foundations

Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasurableSpace