Theorems · Theorem · measure theory

ContinuousMap.memLp

∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} {p : ENNReal} (μ : MeasureTheory.Measure α)
  [inst : TopologicalSpace α] [BorelSpace α] [inst_2 : NormedAddCommGroup E] [SecondCountableTopologyEither α E]
  [CompactSpace α] [MeasureTheory.IsFiniteMeasure μ] [Fact (1 ≤ p)] (𝕜' : Type u_5) [inst_7 : NormedField 𝕜']
  [NormedSpace 𝕜' E] (f : C(α, E)), MeasureTheory.MemLp (⇑f) p μ

Defined in

Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions

Cited by

0 results in Mathlib

Foundations

Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceNormedAddCommGroupSecondCountableTopologyEitherCompactSpaceMeasureTheory.IsFiniteMeasureFactNormedFieldNormedSpace