Theorems · Theorem · functional analysis

MeasureTheory.Lp.norm_compMeasurePreserving

∀ {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} {f : α → β}
  (g : ↥(MeasureTheory.Lp E p μb)) (hf : MeasureTheory.MeasurePreserving f μ μb),
  ‖(MeasureTheory.Lp.compMeasurePreserving f hf) g‖ = ‖g‖

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

5 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupMeasurableSpace