Theorems · Theorem · functional analysis

MeasureTheory.memLp_map_measure_iff

∀ {α : Type u_1} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} {ε : Type u_7}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] {β : Type u_8} {mβ : MeasurableSpace β} {f : α → β}
  {g : β → ε},
  MeasureTheory.AEStronglyMeasurable g (MeasureTheory.Measure.map f μ) →
    AEMeasurable f μ → (MeasureTheory.MemLp g p (MeasureTheory.Measure.map f μ) ↔ MeasureTheory.MemLp (g ∘ f) p μ)

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

10 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENorm