Theorems · Theorem · measure theory

BoundedContinuousFunction.coeFn_toLp

∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} (p : ENNReal) (μ : MeasureTheory.Measure α)
  [inst : TopologicalSpace α] [inst_1 : BorelSpace α] [inst_2 : NormedAddCommGroup E]
  [inst_3 : SecondCountableTopologyEither α E] [inst_4 : MeasureTheory.IsFiniteMeasure μ] (𝕜 : Type u_3)
  [inst_5 : Fact (1 ≤ p)] [inst_6 : NormedRing 𝕜] [inst_7 : Module 𝕜 E] [inst_8 : IsBoundedSMul 𝕜 E]
  (f : BoundedContinuousFunction α E), ↑↑((BoundedContinuousFunction.toLp p μ 𝕜) f) =ᵐ[μ] ⇑f

Defined in

Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions

Cited by

2 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBorelSpaceNormedAddCommGroupSecondCountableTopologyEitherMeasureTheory.IsFiniteMeasureFactNormedRingModuleIsBoundedSMul