Theorems · Theorem · measure theory

MeasureTheory.MemLp.comp_fst

∀ {α : Type u_1} {β : Type u_2} {ε : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  [inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] {μ : MeasureTheory.Measure α} {p : ENNReal} {f : α → ε},
  MeasureTheory.MemLp f p μ →
    ∀ (ν : MeasureTheory.Measure β) [MeasureTheory.IsFiniteMeasure ν], MeasureTheory.MemLp (fun x => f x.1) p (μ.prod ν)

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Prod

Cited by

4 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceContinuousENormMeasureTheory.IsFiniteMeasure